%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL157-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 17:24:34 EDT 2024

% Result   : Unsatisfiable 1.64s 1.87s
% Output   : Proof 2.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : LCL157-1 : TPTP v8.2.0. Released v1.0.0.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n021.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon May 27 23:08:54 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.51  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.64/1.87  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.zmR6qYeA2M/cvc5---1.0.5_18335.smt2
% 1.64/1.87  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.zmR6qYeA2M/cvc5---1.0.5_18335.smt2
% 2.33/2.57  (assume a0 (forall ((X $$unsorted)) (= (tptp.implies tptp.truth X) X)))
% 2.33/2.57  (assume a1 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))) tptp.truth)))
% 2.33/2.57  (assume a2 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 2.33/2.57  (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)) tptp.truth)))
% 2.33/2.57  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.33/2.57  (assume a5 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z)))))
% 2.33/2.57  (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.33/2.57  (assume a7 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.33/2.57  (assume a8 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.33/2.57  (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.33/2.57  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))))
% 2.33/2.57  (assume a11 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))))
% 2.33/2.57  (assume a12 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.33/2.57  (assume a13 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))))
% 2.33/2.57  (assume a14 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))))
% 2.33/2.57  (assume a15 (= (tptp.not tptp.truth) tptp.falsehood))
% 2.33/2.57  (assume a16 (not (= (tptp.and_star tptp.x tptp.falsehood) tptp.falsehood)))
% 2.33/2.57  (step t1 (cl (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (not (= tptp.falsehood (tptp.not tptp.truth))) (not (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (not (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))) (not (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) (not (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x)))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) (not (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (not (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= tptp.truth (tptp.implies tptp.truth tptp.truth))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (not (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (not (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) (not (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) (not (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) (not (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))) (not (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= tptp.x (tptp.implies tptp.truth tptp.x))) (not (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (not (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) (not (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) (not (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) (not (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) (not (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) (not (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) (not (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) (not (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) :rule and_neg)
% 2.33/2.57  (step t2 (cl (=> (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) :rule implies_neg1)
% 2.33/2.57  (anchor :step t3)
% 2.33/2.57  (assume t3.a0 (= tptp.falsehood (tptp.not tptp.truth)))
% 2.33/2.57  (assume t3.a1 (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a2 (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.a3 (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.a4 (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)))
% 2.33/2.57  (assume t3.a5 (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)))
% 2.33/2.57  (assume t3.a6 (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a7 (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))))
% 2.33/2.57  (assume t3.a8 (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.a9 (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.a10 (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.a11 (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))
% 2.33/2.57  (assume t3.a12 (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a13 (= tptp.truth (tptp.implies tptp.truth tptp.truth)))
% 2.33/2.57  (assume t3.a14 (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))))
% 2.33/2.57  (assume t3.a15 (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))))
% 2.33/2.57  (assume t3.a16 (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.a17 (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.a18 (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.a19 (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)))
% 2.33/2.57  (assume t3.a20 (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.a21 (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.a22 (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.a23 (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))))
% 2.33/2.57  (assume t3.a24 (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.a25 (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.a26 (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.a27 (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))))
% 2.33/2.57  (assume t3.a28 (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a29 (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))
% 2.33/2.57  (assume t3.a30 (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.a31 (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.a32 (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.a33 (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))))
% 2.33/2.57  (assume t3.a34 (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))
% 2.33/2.57  (assume t3.a35 (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)))
% 2.33/2.57  (assume t3.a36 (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)))
% 2.33/2.57  (assume t3.a37 (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a38 (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.a39 (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.a40 (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))))
% 2.33/2.57  (assume t3.a41 (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a42 (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)))
% 2.33/2.57  (assume t3.a43 (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))))
% 2.33/2.57  (assume t3.a44 (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.a45 (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))))
% 2.33/2.57  (assume t3.a46 (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.a47 (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.a48 (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)))
% 2.33/2.57  (assume t3.a49 (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))))
% 2.33/2.57  (assume t3.a50 (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))))
% 2.33/2.57  (assume t3.a51 (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.a52 (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a53 (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)))
% 2.33/2.57  (assume t3.a54 (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.a55 (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.a56 (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))))
% 2.33/2.57  (assume t3.a57 (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))
% 2.33/2.57  (assume t3.a58 (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a59 (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))))
% 2.33/2.57  (assume t3.a60 (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.a61 (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))))
% 2.33/2.57  (assume t3.a62 (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.a63 (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))))
% 2.33/2.57  (assume t3.a64 (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a65 (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.a66 (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.a67 (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.a68 (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a69 (= tptp.x (tptp.implies tptp.truth tptp.x)))
% 2.33/2.57  (assume t3.a70 (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.a71 (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.a72 (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a73 (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.a74 (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a75 (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.a76 (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))
% 2.33/2.57  (assume t3.a77 (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.a78 (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.a79 (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)))
% 2.33/2.57  (assume t3.a80 (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.a81 (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)))
% 2.33/2.57  (assume t3.a82 (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.a83 (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.a84 (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))
% 2.33/2.57  (assume t3.a85 (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.a86 (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.a87 (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))
% 2.33/2.57  (assume t3.a88 (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.a89 (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))
% 2.33/2.57  (assume t3.a90 (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.a91 (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))
% 2.33/2.57  (assume t3.a92 (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))))
% 2.33/2.57  (assume t3.a93 (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))))
% 2.33/2.57  (assume t3.a94 (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.a95 (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.a96 (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))
% 2.33/2.57  (assume t3.a97 (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.a98 (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))
% 2.33/2.57  (assume t3.a99 (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.a100 (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.a101 (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.a102 (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.a103 (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))
% 2.33/2.57  (assume t3.a104 (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))))
% 2.33/2.57  (assume t3.a105 (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.a106 (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))))
% 2.33/2.57  (assume t3.a107 (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)))
% 2.33/2.57  (assume t3.a108 (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))))
% 2.33/2.57  (assume t3.a109 (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))))
% 2.33/2.57  (assume t3.a110 (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)))
% 2.33/2.57  (assume t3.a111 (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.a112 (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))
% 2.33/2.57  (assume t3.a113 (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.a114 (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))))
% 2.33/2.57  (assume t3.a115 (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))))
% 2.33/2.57  (assume t3.a116 (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))))
% 2.33/2.57  (assume t3.a117 (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.a118 (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))))
% 2.33/2.57  (assume t3.a119 (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.a120 (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.a121 (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))))
% 2.33/2.57  (assume t3.a122 (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)))
% 2.33/2.57  (assume t3.a123 (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.a124 (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.a125 (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))
% 2.33/2.57  (assume t3.a126 (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.a127 (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))
% 2.33/2.57  (step t3.t1 (cl (=> (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) :rule implies_neg1)
% 2.33/2.57  (anchor :step t3.t2)
% 2.33/2.57  (assume t3.t2.a0 (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))
% 2.33/2.57  (assume t3.t2.a1 (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)))
% 2.33/2.57  (assume t3.t2.a2 (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.t2.a3 (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.t2.a4 (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)))
% 2.33/2.57  (assume t3.t2.a5 (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.t2.a6 (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)))
% 2.33/2.57  (assume t3.t2.a7 (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.t2.a8 (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.t2.a9 (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))))
% 2.33/2.57  (assume t3.t2.a10 (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.t2.a11 (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.t2.a12 (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a13 (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))))
% 2.33/2.57  (assume t3.t2.a14 (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.t2.a15 (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))
% 2.33/2.57  (assume t3.t2.a16 (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.t2.a17 (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.t2.a18 (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.t2.a19 (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))))
% 2.33/2.57  (assume t3.t2.a20 (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))
% 2.33/2.57  (assume t3.t2.a21 (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.t2.a22 (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.t2.a23 (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.t2.a24 (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))
% 2.33/2.57  (assume t3.t2.a25 (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.t2.a26 (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))))
% 2.33/2.57  (assume t3.t2.a27 (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.t2.a28 (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.t2.a29 (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.t2.a30 (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.t2.a31 (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.t2.a32 (= tptp.x (tptp.implies tptp.truth tptp.x)))
% 2.33/2.57  (assume t3.t2.a33 (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a34 (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)))
% 2.33/2.57  (assume t3.t2.a35 (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a36 (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.t2.a37 (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.t2.a38 (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.t2.a39 (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.t2.a40 (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.t2.a41 (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)))
% 2.33/2.57  (assume t3.t2.a42 (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.t2.a43 (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.t2.a44 (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.t2.a45 (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)))
% 2.33/2.57  (assume t3.t2.a46 (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a47 (= tptp.falsehood (tptp.not tptp.truth)))
% 2.33/2.57  (assume t3.t2.a48 (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.t2.a49 (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))))
% 2.33/2.57  (assume t3.t2.a50 (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.t2.a51 (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.t2.a52 (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.t2.a53 (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a54 (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.t2.a55 (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a56 (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))))
% 2.33/2.57  (assume t3.t2.a57 (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))))
% 2.33/2.57  (assume t3.t2.a58 (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))
% 2.33/2.57  (assume t3.t2.a59 (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))))
% 2.33/2.57  (assume t3.t2.a60 (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.t2.a61 (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a62 (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)))
% 2.33/2.57  (assume t3.t2.a63 (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.t2.a64 (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.t2.a65 (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)))
% 2.33/2.57  (assume t3.t2.a66 (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))))
% 2.33/2.57  (assume t3.t2.a67 (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))
% 2.33/2.57  (assume t3.t2.a68 (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.t2.a69 (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.t2.a70 (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))
% 2.33/2.57  (assume t3.t2.a71 (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.t2.a72 (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))
% 2.33/2.57  (assume t3.t2.a73 (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)))
% 2.33/2.57  (assume t3.t2.a74 (= tptp.truth (tptp.implies tptp.truth tptp.truth)))
% 2.33/2.57  (assume t3.t2.a75 (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)))
% 2.33/2.57  (assume t3.t2.a76 (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))))
% 2.33/2.57  (assume t3.t2.a77 (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.t2.a78 (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.t2.a79 (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.t2.a80 (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))))
% 2.33/2.57  (assume t3.t2.a81 (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))))
% 2.33/2.57  (assume t3.t2.a82 (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.t2.a83 (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))
% 2.33/2.57  (assume t3.t2.a84 (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.t2.a85 (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))
% 2.33/2.57  (assume t3.t2.a86 (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a87 (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))))
% 2.33/2.57  (assume t3.t2.a88 (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.t2.a89 (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))))
% 2.33/2.57  (assume t3.t2.a90 (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a91 (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.t2.a92 (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))
% 2.33/2.57  (assume t3.t2.a93 (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a94 (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))))
% 2.33/2.57  (assume t3.t2.a95 (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))
% 2.33/2.57  (assume t3.t2.a96 (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))
% 2.33/2.57  (assume t3.t2.a97 (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.t2.a98 (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.t2.a99 (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))))
% 2.33/2.57  (assume t3.t2.a100 (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))))
% 2.33/2.57  (assume t3.t2.a101 (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.t2.a102 (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.t2.a103 (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))))
% 2.33/2.57  (assume t3.t2.a104 (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))))
% 2.33/2.57  (assume t3.t2.a105 (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.t2.a106 (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))
% 2.33/2.57  (assume t3.t2.a107 (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))))
% 2.33/2.57  (assume t3.t2.a108 (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))))
% 2.33/2.57  (assume t3.t2.a109 (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))))
% 2.33/2.57  (assume t3.t2.a110 (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))))
% 2.33/2.57  (assume t3.t2.a111 (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a112 (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a113 (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)))
% 2.33/2.57  (assume t3.t2.a114 (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a115 (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))))
% 2.33/2.57  (assume t3.t2.a116 (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))
% 2.33/2.57  (assume t3.t2.a117 (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))
% 2.33/2.57  (assume t3.t2.a118 (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)))
% 2.33/2.57  (assume t3.t2.a119 (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.33/2.57  (assume t3.t2.a120 (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.33/2.57  (assume t3.t2.a121 (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))
% 2.33/2.57  (assume t3.t2.a122 (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.33/2.57  (assume t3.t2.a123 (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))))
% 2.33/2.57  (assume t3.t2.a124 (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)))
% 2.33/2.57  (assume t3.t2.a125 (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))))
% 2.33/2.57  (assume t3.t2.a126 (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))))
% 2.33/2.57  (assume t3.t2.a127 (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))
% 2.33/2.57  (step t3.t2.t1 (cl (= (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.a67))
% 2.33/2.57  (step t3.t2.t2 (cl (= tptp.truth tptp.truth)) :rule refl)
% 2.33/2.57  (step t3.t2.t3 (cl (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule symm :premises (t3.t2.a75))
% 2.33/2.57  (step t3.t2.t4 (cl (= (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.a25))
% 2.33/2.57  (step t3.t2.t5 (cl (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t4))
% 2.33/2.57  (step t3.t2.t6 (cl (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule trans :premises (t3.t2.t3 t3.t2.t5))
% 2.33/2.57  (step t3.t2.t7 (cl (= (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.t2 t3.t2.t6))
% 2.33/2.57  (step t3.t2.t8 (cl (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) :rule symm :premises (t3.t2.t7))
% 2.33/2.57  (step t3.t2.t9 (cl (= (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)) (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x))) :rule symm :premises (t3.t2.a115))
% 2.33/2.57  (step t3.t2.t10 (cl (= (tptp.not tptp.truth) tptp.falsehood)) :rule symm :premises (t3.t2.a47))
% 2.33/2.57  (step t3.t2.t11 (cl (= (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.a26))
% 2.33/2.57  (step t3.t2.t12 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.t11))
% 2.33/2.57  (step t3.t2.t13 (cl (= (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.falsehood))) :rule cong :premises (t3.t2.t10))
% 2.33/2.57  (step t3.t2.t14 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))) :rule cong :premises (t3.t2.t10 t3.t2.t13))
% 2.33/2.57  (step t3.t2.t15 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.a42))
% 2.33/2.57  (step t3.t2.t16 (cl (= (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) :rule symm :premises (t3.t2.a97))
% 2.33/2.57  (step t3.t2.t17 (cl (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.t16))
% 2.33/2.57  (step t3.t2.t18 (cl (= (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t2 t3.t2.t17))
% 2.33/2.57  (step t3.t2.t19 (cl (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule trans :premises (t3.t2.t17 t3.t2.t18))
% 2.33/2.57  (step t3.t2.t20 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t19 t3.t2.t17))
% 2.33/2.57  (step t3.t2.t21 (cl (= (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth))) :rule symm :premises (t3.t2.a8))
% 2.33/2.57  (step t3.t2.t22 (cl (= (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) :rule refl)
% 2.33/2.57  (step t3.t2.t23 (cl (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)) tptp.truth)) :rule symm :premises (t3.t2.a59))
% 2.33/2.57  (step t3.t2.t24 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) :rule symm :premises (t3.t2.t23))
% 2.33/2.57  (step t3.t2.t25 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) :rule refl)
% 2.33/2.57  (step t3.t2.t26 (cl (= (tptp.implies tptp.truth tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t2 t3.t2.a47))
% 2.33/2.57  (step t3.t2.t27 (cl (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t25 t3.t2.t26))
% 2.33/2.57  (step t3.t2.t28 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) :rule trans :premises (t3.t2.t24 t3.t2.t27))
% 2.33/2.57  (step t3.t2.t29 (cl (= (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) :rule cong :premises (t3.t2.t22 t3.t2.t28))
% 2.33/2.57  (step t3.t2.t30 (cl (= (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))) tptp.truth)) :rule symm :premises (t3.t2.a76))
% 2.33/2.57  (step t3.t2.t31 (cl (= (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth)) :rule trans :premises (t3.t2.t29 t3.t2.t30))
% 2.33/2.57  (step t3.t2.t32 (cl (= (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule trans :premises (t3.t2.t31 t3.t2.a29))
% 2.33/2.57  (step t3.t2.t33 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.t32 t3.t2.a29))
% 2.33/2.57  (step t3.t2.t34 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))) tptp.truth)) :rule symm :premises (t3.t2.a29))
% 2.33/2.57  (step t3.t2.t35 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth tptp.truth))) :rule cong :premises (t3.t2.t34 t3.t2.t34))
% 2.33/2.57  (step t3.t2.t36 (cl (= (tptp.implies tptp.truth tptp.truth) tptp.truth)) :rule symm :premises (t3.t2.a74))
% 2.33/2.57  (step t3.t2.t37 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) tptp.truth)) :rule trans :premises (t3.t2.t14 t3.t2.t15 t3.t2.t20 t3.t2.t21 t3.t2.t33 t3.t2.t35 t3.t2.t36))
% 2.33/2.57  (step t3.t2.t38 (cl (= (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.not tptp.truth))) :rule cong :premises (t3.t2.t37))
% 2.33/2.57  (step t3.t2.t39 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) tptp.falsehood)) :rule trans :premises (t3.t2.t12 t3.t2.t38 t3.t2.t10))
% 2.33/2.57  (step t3.t2.t40 (cl (= tptp.falsehood (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t39))
% 2.33/2.57  (step t3.t2.t41 (cl (= (tptp.and tptp.truth tptp.falsehood) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t2 t3.t2.a47))
% 2.33/2.57  (step t3.t2.t42 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.truth tptp.falsehood))) :rule symm :premises (t3.t2.t41))
% 2.33/2.57  (step t3.t2.t43 (cl (= (tptp.not tptp.truth) (tptp.and tptp.truth tptp.falsehood))) :rule trans :premises (t3.t2.t10 t3.t2.t40 t3.t2.t42))
% 2.33/2.57  (step t3.t2.t44 (cl (= tptp.x tptp.x)) :rule refl)
% 2.33/2.57  (step t3.t2.t45 (cl (= (tptp.and (tptp.not tptp.truth) tptp.x) (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x))) :rule cong :premises (t3.t2.t43 t3.t2.t44))
% 2.33/2.57  (step t3.t2.t46 (cl (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and (tptp.not tptp.truth) tptp.x))) :rule symm :premises (t3.t2.t45))
% 2.33/2.57  (step t3.t2.t47 (cl (= (tptp.and (tptp.not tptp.truth) tptp.x) (tptp.and tptp.falsehood tptp.x))) :rule cong :premises (t3.t2.t10 t3.t2.t44))
% 2.33/2.57  (step t3.t2.t48 (cl (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a41))
% 2.33/2.57  (step t3.t2.t49 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))) :rule symm :premises (t3.t2.t48))
% 2.33/2.57  (step t3.t2.t50 (cl (= (tptp.and tptp.x tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t44 t3.t2.a47))
% 2.33/2.57  (step t3.t2.t51 (cl (= (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and tptp.x (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t1 t3.t2.t8 t3.t2.t9 t3.t2.t46 t3.t2.t47 t3.t2.t3 t3.t2.t5 t3.t2.t49 t3.t2.t50))
% 2.33/2.57  (step t3.t2.t52 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t49 t3.t2.t50))
% 2.33/2.57  (step t3.t2.t53 (cl (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.t52))
% 2.33/2.57  (step t3.t2.t54 (cl (= (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule trans :premises (t3.t2.t51 t3.t2.t53))
% 2.33/2.57  (step t3.t2.t55 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.a72))
% 2.33/2.57  (step t3.t2.t56 (cl (= (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.not tptp.falsehood))) :rule cong :premises (t3.t2.t39))
% 2.33/2.57  (step t3.t2.t57 (cl (= (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t56))
% 2.33/2.57  (step t3.t2.t58 (cl (= tptp.truth (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t37))
% 2.33/2.57  (step t3.t2.t59 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) :rule trans :premises (t3.t2.t14 t3.t2.t15))
% 2.33/2.57  (step t3.t2.t60 (cl (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) :rule cong :premises (t3.t2.t13 t3.t2.t10))
% 2.33/2.57  (step t3.t2.t61 (cl (= (tptp.or (tptp.not tptp.falsehood) tptp.falsehood) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t60))
% 2.33/2.57  (step t3.t2.t62 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.a99))
% 2.33/2.57  (step t3.t2.t63 (cl (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t62))
% 2.33/2.57  (step t3.t2.t64 (cl (= (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.not tptp.falsehood)))) :rule cong :premises (t3.t2.t13))
% 2.33/2.57  (step t3.t2.t65 (cl (= (tptp.not tptp.truth) (tptp.not tptp.truth))) :rule refl)
% 2.33/2.57  (step t3.t2.t66 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t64 t3.t2.t65))
% 2.33/2.57  (step t3.t2.t67 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.a42 t3.t2.a6 t3.t2.t61 t3.t2.t63 t3.t2.t66))
% 2.33/2.57  (step t3.t2.t68 (cl (= tptp.truth (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t58 t3.t2.t59 t3.t2.t67))
% 2.33/2.57  (step t3.t2.t69 (cl (= (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t68 t3.t2.t17))
% 2.33/2.57  (step t3.t2.t70 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) tptp.truth)) :rule symm :premises (t3.t2.a22))
% 2.33/2.57  (step t3.t2.t71 (cl (= (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))) tptp.truth)) :rule trans :premises (t3.t2.t56 t3.t2.t17 t3.t2.t69 t3.t2.t70))
% 2.33/2.57  (step t3.t2.t72 (cl (= (tptp.not tptp.falsehood) tptp.truth)) :rule trans :premises (t3.t2.t57 t3.t2.t71))
% 2.33/2.57  (step t3.t2.t73 (cl (= (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) :rule refl)
% 2.33/2.57  (step t3.t2.t74 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.truth (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule cong :premises (t3.t2.t72 t3.t2.t73))
% 2.33/2.57  (step t3.t2.t75 (cl (= tptp.truth (tptp.not tptp.falsehood))) :rule symm :premises (t3.t2.t72))
% 2.33/2.57  (step t3.t2.t76 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.a15))
% 2.33/2.57  (step t3.t2.t77 (cl (= (tptp.not (tptp.not tptp.truth)) tptp.truth)) :rule trans :premises (t3.t2.t13 t3.t2.t17 t3.t2.t69 t3.t2.t70))
% 2.33/2.57  (step t3.t2.t78 (cl (= (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x)))) :rule refl)
% 2.33/2.57  (step t3.t2.t79 (cl (= (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) :rule cong :premises (t3.t2.t77 t3.t2.t78))
% 2.33/2.57  (step t3.t2.t80 (cl (= (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))) :rule symm :premises (t3.t2.a101))
% 2.33/2.57  (step t3.t2.t81 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) :rule trans :premises (t3.t2.a21 t3.t2.a103 t3.t2.t79 t3.t2.t80))
% 2.33/2.57  (step t3.t2.t82 (cl (= (tptp.not (tptp.not tptp.x)) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t81))
% 2.33/2.57  (step t3.t2.t83 (cl (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t82))
% 2.33/2.57  (step t3.t2.t84 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) :rule symm :premises (t3.t2.a33))
% 2.33/2.57  (step t3.t2.t85 (cl (= (tptp.not tptp.x) (tptp.not tptp.x))) :rule refl)
% 2.33/2.57  (step t3.t2.t86 (cl (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.and tptp.x (tptp.not tptp.x)))) :rule symm :premises (t3.t2.a113))
% 2.33/2.57  (step t3.t2.t87 (cl (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) :rule symm :premises (t3.t2.t86))
% 2.33/2.57  (step t3.t2.t88 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (tptp.and (tptp.not tptp.x) tptp.x))) :rule symm :premises (t3.t2.a84))
% 2.33/2.57  (step t3.t2.t89 (cl (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t88))
% 2.33/2.57  (step t3.t2.t90 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.a23))
% 2.33/2.57  (step t3.t2.t91 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.a51))
% 2.33/2.57  (step t3.t2.t92 (cl (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t78 t3.t2.t82))
% 2.33/2.57  (step t3.t2.t93 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) :rule refl)
% 2.33/2.57  (step t3.t2.t94 (cl (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))) (tptp.implies (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t82 t3.t2.t93))
% 2.33/2.57  (step t3.t2.t95 (cl (= (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t13))
% 2.33/2.57  (step t3.t2.t96 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) :rule cong :premises (t3.t2.t95 t3.t2.t78))
% 2.33/2.57  (step t3.t2.t97 (cl (= (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.a103))
% 2.33/2.57  (step t3.t2.t98 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.a21))
% 2.33/2.57  (step t3.t2.t99 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t96 t3.t2.t97 t3.t2.t98))
% 2.33/2.57  (step t3.t2.t100 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t99))
% 2.33/2.57  (step t3.t2.t101 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) :rule cong :premises (t3.t2.t100 t3.t2.t81))
% 2.33/2.57  (step t3.t2.t102 (cl (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) :rule cong :premises (t3.t2.t99 t3.t2.t78))
% 2.33/2.57  (step t3.t2.t103 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.a100))
% 2.33/2.57  (step t3.t2.t104 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t103))
% 2.33/2.57  (step t3.t2.t105 (cl (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t80))
% 2.33/2.57  (step t3.t2.t106 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t104 t3.t2.t105))
% 2.33/2.57  (step t3.t2.t107 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) tptp.truth)) :rule symm :premises (t3.t2.a10))
% 2.33/2.57  (step t3.t2.t108 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) tptp.truth)) :rule trans :premises (t3.t2.t90 t3.t2.t91 t3.t2.t92 t3.t2.t94 t3.t2.t101 t3.t2.t102 t3.t2.t106 t3.t2.t107))
% 2.33/2.57  (step t3.t2.t109 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (tptp.not tptp.truth))) :rule cong :premises (t3.t2.t108))
% 2.33/2.57  (step t3.t2.t110 (cl (= (tptp.not tptp.truth) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.t38))
% 2.33/2.57  (step t3.t2.t111 (cl (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t87 t3.t2.t89 t3.t2.t109 t3.t2.t110 t3.t2.t11))
% 2.33/2.57  (step t3.t2.t112 (cl (= (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t111))
% 2.33/2.57  (step t3.t2.t113 (cl (= (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.truth)) :rule trans :premises (t3.t2.t112 t3.t2.t56 t3.t2.t17 t3.t2.t69 t3.t2.t70))
% 2.33/2.57  (step t3.t2.t114 (cl (= tptp.truth (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t113))
% 2.33/2.57  (step t3.t2.t115 (cl (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t85 t3.t2.t114))
% 2.33/2.57  (step t3.t2.t116 (cl (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) :rule trans :premises (t3.t2.t83 t3.t2.t84 t3.t2.t115))
% 2.33/2.57  (step t3.t2.t117 (cl (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) :rule cong :premises (t3.t2.t44 t3.t2.t116))
% 2.33/2.57  (step t3.t2.t118 (cl (= (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))) (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.a19))
% 2.33/2.57  (step t3.t2.t119 (cl (= (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))) :rule refl)
% 2.33/2.57  (step t3.t2.t120 (cl (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.a64 t3.t2.t119))
% 2.33/2.57  (step t3.t2.t121 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.not tptp.x)))) :rule symm :premises (t3.t2.a64))
% 2.33/2.57  (step t3.t2.t122 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) :rule symm :premises (t3.t2.a60))
% 2.33/2.57  (step t3.t2.t123 (cl (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.a73))
% 2.33/2.57  (step t3.t2.t124 (cl (= tptp.falsehood (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule trans :premises (t3.t2.t40 t3.t2.t12))
% 2.33/2.57  (step t3.t2.t125 (cl (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule cong :premises (t3.t2.t124 t3.t2.t57))
% 2.33/2.57  (step t3.t2.t126 (cl (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth)))) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule cong :premises (t3.t2.t38 t3.t2.t71))
% 2.33/2.57  (step t3.t2.t127 (cl (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.a70))
% 2.33/2.57  (step t3.t2.t128 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t122 t3.t2.t123 t3.t2.t125 t3.t2.t126 t3.t2.t127))
% 2.33/2.57  (step t3.t2.t129 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.t128))
% 2.33/2.57  (step t3.t2.t130 (cl (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule trans :premises (t3.t2.a73 t3.t2.a60))
% 2.33/2.57  (step t3.t2.t131 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.t130))
% 2.33/2.57  (step t3.t2.t132 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and tptp.falsehood (tptp.not tptp.falsehood)))) :rule trans :premises (t3.t2.t121 t3.t2.t111 t3.t2.t129 t3.t2.t131))
% 2.33/2.57  (step t3.t2.t133 (cl (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t132 t3.t2.t119))
% 2.33/2.57  (step t3.t2.t134 (cl (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.not tptp.truth))) :rule trans :premises (t3.t2.t130 t3.t2.t128 t3.t2.t39 t3.t2.a47))
% 2.33/2.57  (step t3.t2.t135 (cl (= (tptp.and (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule cong :premises (t3.t2.t134 t3.t2.t113))
% 2.33/2.57  (step t3.t2.t136 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t76 t3.t2.t117 t3.t2.t118 t3.t2.t120 t3.t2.t133 t3.t2.t135 t3.t2.t127))
% 2.33/2.57  (step t3.t2.t137 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) tptp.falsehood)) :rule trans :premises (t3.t2.t136 t3.t2.t39))
% 2.33/2.57  (step t3.t2.t138 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth))) :rule symm :premises (t3.t2.a112))
% 2.33/2.57  (step t3.t2.t139 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t138 t3.t2.a82 t3.t2.t8 t3.t2.t9 t3.t2.t46 t3.t2.t47 t3.t2.t3 t3.t2.t5 t3.t2.t49 t3.t2.t50))
% 2.33/2.57  (step t3.t2.t140 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t137 t3.t2.t139))
% 2.33/2.57  (step t3.t2.t141 (cl (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.a46))
% 2.33/2.57  (step t3.t2.t142 (cl (= (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))) :rule refl)
% 2.33/2.57  (step t3.t2.t143 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.t142 t3.t2.t53))
% 2.33/2.57  (step t3.t2.t144 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t72 t3.t2.t52))
% 2.33/2.57  (step t3.t2.t145 (cl (= (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.a55))
% 2.33/2.57  (step t3.t2.t146 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t140 t3.t2.t141 t3.t2.t143 t3.t2.t144 t3.t2.t145))
% 2.33/2.57  (step t3.t2.t147 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t146))
% 2.33/2.57  (step t3.t2.t148 (cl (= (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) :rule symm :premises (t3.t2.t147))
% 2.33/2.57  (step t3.t2.t149 (cl (= (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t64))
% 2.33/2.57  (step t3.t2.t150 (cl (= tptp.truth (tptp.not (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t77))
% 2.33/2.57  (step t3.t2.t151 (cl (= (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t150))
% 2.33/2.57  (step t3.t2.t152 (cl (= (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) :rule symm :premises (t3.t2.t151))
% 2.33/2.57  (step t3.t2.t153 (cl (= (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t149 t3.t2.t152 t3.t2.t110 t3.t2.t11))
% 2.33/2.57  (step t3.t2.t154 (cl (= (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t153))
% 2.33/2.57  (step t3.t2.t155 (cl (= (tptp.not (tptp.not (tptp.not tptp.falsehood))) tptp.truth)) :rule trans :premises (t3.t2.t154 t3.t2.t56 t3.t2.t17 t3.t2.t69 t3.t2.t70))
% 2.33/2.57  (step t3.t2.t156 (cl (= (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) :rule cong :premises (t3.t2.t155))
% 2.33/2.57  (step t3.t2.t157 (cl (= (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) tptp.falsehood)) :rule trans :premises (t3.t2.t156 t3.t2.t10))
% 2.33/2.57  (step t3.t2.t158 (cl (= (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t157 t3.t2.t52))
% 2.33/2.57  (step t3.t2.t159 (cl (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.t140))
% 2.33/2.57  (step t3.t2.t160 (cl (= (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) :rule trans :premises (t3.t2.t158 t3.t2.t159))
% 2.33/2.57  (step t3.t2.t161 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) :rule cong :premises (t3.t2.t160))
% 2.33/2.57  (step t3.t2.t162 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.t161))
% 2.33/2.57  (step t3.t2.t163 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a88))
% 2.33/2.57  (step t3.t2.t164 (cl (= tptp.truth (tptp.not (tptp.not (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.t155))
% 2.33/2.57  (step t3.t2.t165 (cl (= (tptp.not tptp.falsehood) (tptp.not (tptp.not (tptp.not tptp.falsehood))))) :rule trans :premises (t3.t2.t57 t3.t2.t71 t3.t2.t164))
% 2.33/2.57  (step t3.t2.t166 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) :rule refl)
% 2.33/2.57  (step t3.t2.t167 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t165 t3.t2.t166))
% 2.33/2.57  (step t3.t2.t168 (cl (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.t167))
% 2.33/2.57  (step t3.t2.t169 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t72 t3.t2.t166))
% 2.33/2.57  (step t3.t2.t170 (cl (= (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule trans :premises (t3.t2.t148 t3.t2.t162 t3.t2.t163 t3.t2.t168 t3.t2.t169))
% 2.33/2.57  (step t3.t2.t171 (cl (= (tptp.and tptp.truth (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.t75 t3.t2.t170))
% 2.33/2.57  (step t3.t2.t172 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a117))
% 2.33/2.57  (step t3.t2.t173 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.t69))
% 2.33/2.57  (step t3.t2.t174 (cl (= tptp.falsehood (tptp.implies tptp.truth (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.a45 t3.t2.t26))
% 2.33/2.57  (step t3.t2.t175 (cl (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) tptp.falsehood) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t25 t3.t2.t174))
% 2.33/2.57  (step t3.t2.t176 (cl (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) :rule symm :premises (t3.t2.t27))
% 2.33/2.57  (step t3.t2.t177 (cl (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) tptp.falsehood) tptp.truth)) :rule trans :premises (t3.t2.t175 t3.t2.t176 t3.t2.t23))
% 2.33/2.57  (step t3.t2.t178 (cl (= tptp.falsehood tptp.falsehood)) :rule refl)
% 2.33/2.57  (step t3.t2.t179 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) tptp.falsehood) tptp.falsehood) (tptp.implies tptp.truth tptp.falsehood))) :rule cong :premises (t3.t2.t177 t3.t2.t178))
% 2.33/2.57  (step t3.t2.t180 (cl (= (tptp.implies tptp.truth tptp.falsehood) (tptp.implies (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) tptp.falsehood) tptp.falsehood))) :rule symm :premises (t3.t2.t179))
% 2.33/2.57  (step t3.t2.t181 (cl (= (tptp.or (tptp.not tptp.falsehood) tptp.falsehood) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.a6))
% 2.33/2.57  (step t3.t2.t182 (cl (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) :rule trans :premises (t3.t2.t60 t3.t2.t181 t3.t2.t15))
% 2.33/2.57  (step t3.t2.t183 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t59))
% 2.33/2.57  (step t3.t2.t184 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) tptp.falsehood))) :rule symm :premises (t3.t2.t177))
% 2.33/2.57  (step t3.t2.t185 (cl (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) tptp.falsehood))) :rule trans :premises (t3.t2.t182 t3.t2.t183 t3.t2.t37 t3.t2.t184))
% 2.33/2.57  (step t3.t2.t186 (cl (= (tptp.and (tptp.not tptp.truth) tptp.truth) tptp.falsehood)) :rule trans :premises (t3.t2.t127 t3.t2.t12 t3.t2.t38 t3.t2.t10))
% 2.33/2.57  (step t3.t2.t187 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.implies (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) tptp.falsehood) tptp.falsehood))) :rule cong :premises (t3.t2.t185 t3.t2.t186))
% 2.33/2.57  (step t3.t2.t188 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) tptp.falsehood) tptp.falsehood) (tptp.implies (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule symm :premises (t3.t2.t187))
% 2.33/2.57  (step t3.t2.t189 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t14))
% 2.33/2.57  (step t3.t2.t190 (cl (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) :rule trans :premises (t3.t2.t60 t3.t2.t181 t3.t2.t189))
% 2.33/2.57  (step t3.t2.t191 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t190))
% 2.33/2.57  (step t3.t2.t192 (cl (= (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) :rule trans :premises (t3.t2.t11 t3.t2.a70 t3.t2.a53))
% 2.33/2.57  (step t3.t2.t193 (cl (= (tptp.and (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) :rule cong :premises (t3.t2.t191 t3.t2.t192))
% 2.33/2.57  (step t3.t2.t194 (cl (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) tptp.truth)) :rule trans :premises (t3.t2.t190 t3.t2.t37))
% 2.33/2.57  (step t3.t2.t195 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule symm :premises (t3.t2.a53))
% 2.33/2.57  (step t3.t2.t196 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) tptp.falsehood)) :rule trans :premises (t3.t2.t195 t3.t2.t127 t3.t2.t12 t3.t2.t38 t3.t2.t10))
% 2.33/2.57  (step t3.t2.t197 (cl (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (tptp.and tptp.truth tptp.falsehood))) :rule cong :premises (t3.t2.t194 t3.t2.t196))
% 2.33/2.57  (step t3.t2.t198 (cl (= (tptp.and (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t193 t3.t2.t197 t3.t2.t41))
% 2.33/2.57  (step t3.t2.t199 (cl (= (tptp.not (tptp.and (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t198))
% 2.33/2.57  (step t3.t2.t200 (cl (= (tptp.not (tptp.and (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (tptp.not tptp.falsehood))) :rule trans :premises (t3.t2.t199 t3.t2.t56))
% 2.33/2.57  (step t3.t2.t201 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t182))
% 2.33/2.57  (step t3.t2.t202 (cl (= (tptp.not (tptp.and (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t200 t3.t2.t95 t3.t2.t77 t3.t2.t58 t3.t2.t59 t3.t2.t201))
% 2.33/2.57  (step t3.t2.t203 (cl (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule cong :premises (t3.t2.t38 t3.t2.t37))
% 2.33/2.57  (step t3.t2.t204 (cl (= (tptp.implies (tptp.not (tptp.and (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (tptp.implies (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule cong :premises (t3.t2.t202 t3.t2.t203))
% 2.33/2.57  (step t3.t2.t205 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.implies (tptp.not (tptp.and (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))))) :rule symm :premises (t3.t2.t204))
% 2.33/2.57  (step t3.t2.t206 (cl (= (tptp.not tptp.falsehood) (tptp.not (tptp.and (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))))) :rule symm :premises (t3.t2.t200))
% 2.33/2.57  (step t3.t2.t207 (cl (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.t203))
% 2.33/2.57  (step t3.t2.t208 (cl (= tptp.falsehood (tptp.and (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule trans :premises (t3.t2.a47 t3.t2.t110 t3.t2.t11 t3.t2.a70 t3.t2.t207))
% 2.33/2.57  (step t3.t2.t209 (cl (= (tptp.implies (tptp.not tptp.falsehood) tptp.falsehood) (tptp.implies (tptp.not (tptp.and (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))))) :rule cong :premises (t3.t2.t206 t3.t2.t208))
% 2.33/2.57  (step t3.t2.t210 (cl (= (tptp.implies (tptp.not (tptp.and (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (tptp.implies (tptp.not tptp.falsehood) tptp.falsehood))) :rule symm :premises (t3.t2.t209))
% 2.33/2.57  (step t3.t2.t211 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) tptp.falsehood))) :rule cong :premises (t3.t2.t142 t3.t2.t10))
% 2.33/2.57  (step t3.t2.t212 (cl (= (tptp.implies (tptp.not tptp.falsehood) tptp.falsehood) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t211))
% 2.33/2.57  (step t3.t2.t213 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t10 t3.t2.t65))
% 2.33/2.57  (step t3.t2.t214 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t213))
% 2.33/2.57  (step t3.t2.t215 (cl (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not tptp.truth))) :rule trans :premises (t3.t2.t127 t3.t2.t39 t3.t2.a47))
% 2.33/2.57  (step t3.t2.t216 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not tptp.truth))) :rule trans :premises (t3.t2.t12 t3.t2.t38))
% 2.33/2.57  (step t3.t2.t217 (cl (= (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.or (tptp.not tptp.truth) (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t215 t3.t2.t216))
% 2.33/2.57  (step t3.t2.t218 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t217))
% 2.33/2.57  (step t3.t2.t219 (cl (= (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule symm :premises (t3.t2.a12))
% 2.33/2.57  (step t3.t2.t220 (cl (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.xor tptp.truth tptp.truth))) :rule symm :premises (t3.t2.a20))
% 2.33/2.57  (step t3.t2.t221 (cl (= (tptp.xor (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth)))) (tptp.xor tptp.truth tptp.truth))) :rule cong :premises (t3.t2.t37 t3.t2.t71))
% 2.33/2.57  (step t3.t2.t222 (cl (= (tptp.xor tptp.truth tptp.truth) (tptp.xor (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.t221))
% 2.33/2.57  (step t3.t2.t223 (cl (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.xor (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule cong :premises (t3.t2.t58 t3.t2.t57))
% 2.33/2.57  (step t3.t2.t224 (cl (= (tptp.xor (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth)))) (tptp.xor tptp.truth (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.t223))
% 2.33/2.57  (step t3.t2.t225 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) :rule cong :premises (t3.t2.t142 t3.t2.t10))
% 2.33/2.57  (step t3.t2.t226 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and tptp.falsehood (tptp.not tptp.falsehood)))) :rule trans :premises (t3.t2.t225 t3.t2.t123))
% 2.33/2.57  (step t3.t2.t227 (cl (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) :rule cong :premises (t3.t2.a47 t3.t2.t142))
% 2.33/2.57  (step t3.t2.t228 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) :rule trans :premises (t3.t2.t226 t3.t2.t227))
% 2.33/2.57  (step t3.t2.t229 (cl (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) :rule symm :premises (t3.t2.a5))
% 2.33/2.57  (step t3.t2.t230 (cl (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.t229))
% 2.33/2.57  (step t3.t2.t231 (cl (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.t228 t3.t2.t230))
% 2.33/2.57  (step t3.t2.t232 (cl (= (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule symm :premises (t3.t2.t231))
% 2.33/2.57  (step t3.t2.t233 (cl (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)) (tptp.xor (tptp.not tptp.falsehood) tptp.truth))) :rule symm :premises (t3.t2.a49))
% 2.33/2.57  (step t3.t2.t234 (cl (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.xor (tptp.not tptp.falsehood) tptp.truth))) :rule cong :premises (t3.t2.t142 t3.t2.t72))
% 2.33/2.57  (step t3.t2.t235 (cl (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.t234))
% 2.33/2.57  (step t3.t2.t236 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.a31))
% 2.33/2.57  (step t3.t2.t237 (cl (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a27))
% 2.33/2.57  (step t3.t2.t238 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) :rule trans :premises (t3.t2.t236 t3.t2.t237))
% 2.33/2.57  (step t3.t2.t239 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.t236 t3.t2.t238))
% 2.33/2.57  (step t3.t2.t240 (cl (= (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.t239))
% 2.33/2.57  (step t3.t2.t241 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))))) :rule trans :premises (t3.t2.t12 t3.t2.t38 t3.t2.t10 t3.t2.a45 t3.t2.t180 t3.t2.t188 t3.t2.t205 t3.t2.t210 t3.t2.t212 t3.t2.a9 t3.t2.t214 t3.t2.t218 t3.t2.t219 t3.t2.t220 t3.t2.t222 t3.t2.t224 t3.t2.a14 t3.t2.a18 t3.t2.t232 t3.t2.t233 t3.t2.t235 t3.t2.a44 t3.t2.a52 t3.t2.t240))
% 2.33/2.57  (step t3.t2.t242 (cl (= (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))))) :rule cong :premises (t3.t2.t241))
% 2.33/2.57  (step t3.t2.t243 (cl (= (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a52))
% 2.33/2.57  (step t3.t2.t244 (cl (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.a44))
% 2.33/2.57  (step t3.t2.t245 (cl (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule symm :premises (t3.t2.t233))
% 2.33/2.57  (step t3.t2.t246 (cl (= (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a18))
% 2.33/2.57  (step t3.t2.t247 (cl (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.xor tptp.truth (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.a14))
% 2.33/2.57  (step t3.t2.t248 (cl (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule symm :premises (t3.t2.t220))
% 2.33/2.57  (step t3.t2.t249 (cl (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t219))
% 2.33/2.57  (step t3.t2.t250 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) :rule trans :premises (t3.t2.a70 t3.t2.a53))
% 2.33/2.57  (step t3.t2.t251 (cl (= (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) :rule cong :premises (t3.t2.a53 t3.t2.t250))
% 2.33/2.57  (step t3.t2.t252 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) :rule trans :premises (t3.t2.t239 t3.t2.t243 t3.t2.t244 t3.t2.t234 t3.t2.t245 t3.t2.t231 t3.t2.t246 t3.t2.t247 t3.t2.t223 t3.t2.t221 t3.t2.t248 t3.t2.t249 t3.t2.t251))
% 2.33/2.57  (step t3.t2.t253 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) :rule cong :premises (t3.t2.t252))
% 2.33/2.57  (step t3.t2.t254 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.a57))
% 2.33/2.57  (step t3.t2.t255 (cl (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.and (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) tptp.truth))) :rule cong :premises (t3.t2.t190 t3.t2.t194))
% 2.33/2.57  (step t3.t2.t256 (cl (= (tptp.and (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))) tptp.truth) (tptp.and tptp.truth tptp.truth))) :rule cong :premises (t3.t2.t37 t3.t2.t2))
% 2.33/2.57  (step t3.t2.t257 (cl (= (tptp.and tptp.truth tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))) :rule cong :premises (t3.t2.t2 t3.t2.t75))
% 2.33/2.57  (step t3.t2.t258 (cl (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth))) :rule symm :premises (t3.t2.a3))
% 2.33/2.57  (step t3.t2.t259 (cl (= tptp.truth (tptp.and (tptp.not tptp.falsehood) tptp.truth))) :rule trans :premises (t3.t2.a22 t3.t2.t173 t3.t2.t16 t3.t2.t57 t3.t2.t242 t3.t2.t253 t3.t2.t254 t3.t2.t255 t3.t2.t256 t3.t2.t257 t3.t2.t258))
% 2.33/2.57  (step t3.t2.t260 (cl (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.truth)) :rule symm :premises (t3.t2.t259))
% 2.33/2.57  (step t3.t2.t261 (cl (= tptp.truth (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t71))
% 2.33/2.57  (step t3.t2.t262 (cl (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.not tptp.falsehood))) :rule trans :premises (t3.t2.t260 t3.t2.t261 t3.t2.t56))
% 2.33/2.57  (step t3.t2.t263 (cl (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t262 t3.t2.t166))
% 2.33/2.57  (step t3.t2.t264 (cl (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.t163))
% 2.33/2.57  (step t3.t2.t265 (cl (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t52))
% 2.33/2.57  (step t3.t2.t266 (cl (= (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.t265))
% 2.33/2.57  (step t3.t2.t267 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule trans :premises (t3.t2.t55 t3.t2.t74 t3.t2.t171 t3.t2.t172 t3.t2.t263 t3.t2.t167 t3.t2.t264 t3.t2.t161 t3.t2.t147 t3.t2.t266))
% 2.33/2.57  (step t3.t2.t268 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t54 t3.t2.t267))
% 2.33/2.57  (step t3.t2.t269 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.a30))
% 2.33/2.57  (step t3.t2.t270 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.t269))
% 2.33/2.57  (step t3.t2.t271 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule cong :premises (t3.t2.t265 t3.t2.t265))
% 2.33/2.57  (step t3.t2.t272 (cl (= (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.a120))
% 2.33/2.57  (step t3.t2.t273 (cl (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.t272))
% 2.33/2.57  (step t3.t2.t274 (cl (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.a108))
% 2.33/2.57  (step t3.t2.t275 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.t274))
% 2.33/2.57  (step t3.t2.t276 (cl (= (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule cong :premises (t3.t2.t275 t3.t2.t75))
% 2.33/2.57  (step t3.t2.t277 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.a43))
% 2.33/2.57  (step t3.t2.t278 (cl (= (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) tptp.truth)) :rule trans :premises (t3.t2.t276 t3.t2.t277 t3.t2.t102 t3.t2.t106 t3.t2.t107))
% 2.33/2.57  (step t3.t2.t279 (cl (= tptp.truth (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth))) :rule symm :premises (t3.t2.t278))
% 2.33/2.57  (step t3.t2.t280 (cl (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule refl)
% 2.33/2.57  (step t3.t2.t281 (cl (= (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t279 t3.t2.t280))
% 2.33/2.57  (step t3.t2.t282 (cl (= (tptp.not (tptp.not tptp.truth)) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth))) :rule trans :premises (t3.t2.t77 t3.t2.t279))
% 2.33/2.57  (step t3.t2.t283 (cl (= (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t282 t3.t2.t280))
% 2.33/2.57  (step t3.t2.t284 (cl (= (tptp.implies (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.t283))
% 2.33/2.57  (step t3.t2.t285 (cl (= (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.a37))
% 2.33/2.57  (step t3.t2.t286 (cl (= (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule trans :premises (t3.t2.t266 t3.t2.t273 t3.t2.t281 t3.t2.t284 t3.t2.t285))
% 2.33/2.57  (step t3.t2.t287 (cl (= (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule cong :premises (t3.t2.t286 t3.t2.t286))
% 2.33/2.57  (step t3.t2.t288 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.t285))
% 2.33/2.57  (step t3.t2.t289 (cl (= (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.falsehood))) :rule trans :premises (t3.t2.t278 t3.t2.t75))
% 2.33/2.57  (step t3.t2.t290 (cl (= (tptp.implies (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule cong :premises (t3.t2.t289 t3.t2.t265))
% 2.33/2.57  (step t3.t2.t291 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule trans :premises (t3.t2.t288 t3.t2.t283 t3.t2.t290))
% 2.33/2.57  (step t3.t2.t292 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.a9))
% 2.33/2.57  (step t3.t2.t293 (cl (= (tptp.implies tptp.truth tptp.falsehood) tptp.falsehood)) :rule symm :premises (t3.t2.a45))
% 2.33/2.57  (step t3.t2.t294 (cl (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t249 t3.t2.t217 t3.t2.t213 t3.t2.t292 t3.t2.t211 t3.t2.t209 t3.t2.t204 t3.t2.t187 t3.t2.t179 t3.t2.t293 t3.t2.a47 t3.t2.t110 t3.t2.t11))
% 2.33/2.57  (step t3.t2.t295 (cl (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.not tptp.truth))) :rule trans :premises (t3.t2.t294 t3.t2.t39 t3.t2.a47))
% 2.33/2.57  (step t3.t2.t296 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t280 t3.t2.t295))
% 2.33/2.57  (step t3.t2.t297 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule symm :premises (t3.t2.t296))
% 2.33/2.57  (step t3.t2.t298 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule symm :premises (t3.t2.a111))
% 2.33/2.57  (step t3.t2.t299 (cl (= (tptp.not tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t216))
% 2.33/2.57  (step t3.t2.t300 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t280 t3.t2.t299))
% 2.33/2.57  (step t3.t2.t301 (cl (= (tptp.not tptp.truth) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule symm :premises (t3.t2.t215))
% 2.33/2.57  (step t3.t2.t302 (cl (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule cong :premises (t3.t2.t300 t3.t2.t301))
% 2.33/2.57  (step t3.t2.t303 (cl (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t302))
% 2.33/2.57  (step t3.t2.t304 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t5))
% 2.33/2.57  (step t3.t2.t305 (cl (= (tptp.and tptp.falsehood tptp.x) (tptp.and (tptp.not tptp.truth) tptp.x))) :rule symm :premises (t3.t2.t47))
% 2.33/2.57  (step t3.t2.t306 (cl (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) :rule symm :premises (t3.t2.t9))
% 2.33/2.57  (step t3.t2.t307 (cl (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth))) :rule symm :premises (t3.t2.a82))
% 2.33/2.57  (step t3.t2.t308 (cl (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t138))
% 2.33/2.57  (step t3.t2.t309 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule trans :premises (t3.t2.t304 t3.t2.a75 t3.t2.t305 t3.t2.t45 t3.t2.t306 t3.t2.t7 t3.t2.t307 t3.t2.t308))
% 2.33/2.57  (step t3.t2.t310 (cl (= (tptp.implies (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t309 t3.t2.t65))
% 2.33/2.57  (step t3.t2.t311 (cl (= (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t310))
% 2.33/2.57  (step t3.t2.t312 (cl (= (tptp.implies (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.truth)) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) :rule cong :premises (t3.t2.t52 t3.t2.t10))
% 2.33/2.57  (step t3.t2.t313 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) :rule trans :premises (t3.t2.a92 t3.t2.t297 t3.t2.t298 t3.t2.t303 t3.t2.a80 t3.t2.t311 t3.t2.t312))
% 2.33/2.57  (step t3.t2.t314 (cl (= (tptp.implies (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) :rule cong :premises (t3.t2.t291 t3.t2.t313))
% 2.33/2.57  (step t3.t2.t315 (cl (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)) tptp.truth)) :rule symm :premises (t3.t2.a87))
% 2.33/2.57  (step t3.t2.t316 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) tptp.truth)) :rule trans :premises (t3.t2.t268 t3.t2.t270 t3.t2.t271 t3.t2.t287 t3.t2.t314 t3.t2.t315))
% 2.33/2.57  (step t3.t2.t317 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (tptp.not tptp.truth))) :rule cong :premises (t3.t2.t316))
% 2.33/2.57  (step t3.t2.t318 (cl (= (tptp.not tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule symm :premises (t3.t2.t317))
% 2.33/2.57  (step t3.t2.t319 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule symm :premises (t3.t2.t268))
% 2.33/2.57  (step t3.t2.t320 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule cong :premises (t3.t2.t319))
% 2.33/2.57  (step t3.t2.t321 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule symm :premises (t3.t2.t320))
% 2.33/2.57  (step t3.t2.t322 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.a121))
% 2.33/2.57  (step t3.t2.t323 (cl (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t6 t3.t2.t166))
% 2.33/2.57  (step t3.t2.t324 (cl (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.t323))
% 2.33/2.57  (step t3.t2.t325 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood tptp.x))) :rule symm :premises (t3.t2.t6))
% 2.33/2.57  (step t3.t2.t326 (cl (= (tptp.and tptp.x tptp.falsehood) (tptp.and tptp.falsehood tptp.x))) :rule trans :premises (t3.t2.t48 t3.t2.t325))
% 2.33/2.57  (step t3.t2.t327 (cl (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t326 t3.t2.t166))
% 2.33/2.57  (step t3.t2.t328 (cl (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.t327))
% 2.33/2.57  (step t3.t2.t329 (cl (= (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood))) :rule symm :premises (t3.t2.a71))
% 2.33/2.57  (step t3.t2.t330 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.t329))
% 2.33/2.57  (step t3.t2.t331 (cl (= (tptp.and tptp.x (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.t44 t3.t2.t330))
% 2.33/2.57  (step t3.t2.t332 (cl (= (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.x (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)))) :rule symm :premises (t3.t2.t331))
% 2.33/2.57  (step t3.t2.t333 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood))) :rule symm :premises (t3.t2.a127))
% 2.33/2.57  (step t3.t2.t334 (cl (= (tptp.and tptp.x (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (tptp.and tptp.x (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)))) :rule cong :premises (t3.t2.t44 t3.t2.t333))
% 2.33/2.57  (step t3.t2.t335 (cl (= (tptp.and tptp.x (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.and tptp.x (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.t334))
% 2.33/2.57  (step t3.t2.t336 (cl (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))))) :rule cong :premises (t3.t2.t75 t3.t2.t78))
% 2.33/2.57  (step t3.t2.t337 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.truth (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t336))
% 2.33/2.57  (step t3.t2.t338 (cl (= (tptp.and tptp.truth (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))) (tptp.and tptp.truth (tptp.not (tptp.not tptp.x))))) :rule cong :premises (t3.t2.t2 t3.t2.t81))
% 2.33/2.57  (step t3.t2.t339 (cl (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.x))) (tptp.and tptp.truth (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t338))
% 2.33/2.57  (step t3.t2.t340 (cl (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.and tptp.truth tptp.x))) :rule cong :premises (t3.t2.t72 t3.t2.t44))
% 2.33/2.57  (step t3.t2.t341 (cl (= (tptp.and tptp.truth tptp.x) (tptp.and (tptp.not tptp.falsehood) tptp.x))) :rule symm :premises (t3.t2.t340))
% 2.33/2.57  (step t3.t2.t342 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))) :rule cong :premises (t3.t2.t10 t3.t2.t85))
% 2.33/2.57  (step t3.t2.t343 (cl (= (tptp.not (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth)))) (tptp.not (tptp.not tptp.falsehood)))) :rule cong :premises (t3.t2.t56))
% 2.33/2.57  (step t3.t2.t344 (cl (= (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.t343))
% 2.33/2.57  (step t3.t2.t345 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule trans :premises (t3.t2.t12 t3.t2.t38 t3.t2.t151 t3.t2.t64 t3.t2.t344))
% 2.33/2.57  (step t3.t2.t346 (cl (= tptp.falsehood (tptp.not (tptp.not tptp.falsehood)))) :rule trans :premises (t3.t2.t40 t3.t2.t345 t3.t2.t343))
% 2.33/2.57  (step t3.t2.t347 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) :rule cong :premises (t3.t2.t346 t3.t2.t85))
% 2.33/2.57  (step t3.t2.t348 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) :rule trans :premises (t3.t2.t342 t3.t2.t347))
% 2.33/2.57  (step t3.t2.t349 (cl (= (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) :rule cong :premises (t3.t2.t348))
% 2.33/2.57  (step t3.t2.t350 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t349))
% 2.33/2.57  (step t3.t2.t351 (cl (= (tptp.implies tptp.truth (tptp.not tptp.x)) (tptp.not tptp.x))) :rule symm :premises (t3.t2.a91))
% 2.33/2.57  (step t3.t2.t352 (cl (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) :rule symm :premises (t3.t2.t351))
% 2.33/2.57  (step t3.t2.t353 (cl (= (tptp.implies tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule cong :premises (t3.t2.t75 t3.t2.t85))
% 2.33/2.57  (step t3.t2.t354 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule symm :premises (t3.t2.a7))
% 2.33/2.57  (step t3.t2.t355 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))) :rule symm :premises (t3.t2.t354))
% 2.33/2.57  (step t3.t2.t356 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.truth) (tptp.not tptp.x)))) :rule symm :premises (t3.t2.t342))
% 2.33/2.57  (step t3.t2.t357 (cl (= (tptp.not tptp.x) (tptp.or (tptp.not tptp.truth) (tptp.not tptp.x)))) :rule trans :premises (t3.t2.t352 t3.t2.t353 t3.t2.t355 t3.t2.t356))
% 2.33/2.57  (step t3.t2.t358 (cl (= (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not tptp.x))))) :rule cong :premises (t3.t2.t357))
% 2.33/2.57  (step t3.t2.t359 (cl (= (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))) :rule symm :premises (t3.t2.t358))
% 2.33/2.57  (step t3.t2.t360 (cl (= (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t79))
% 2.33/2.57  (step t3.t2.t361 (cl (= (tptp.and tptp.truth tptp.x) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t341 t3.t2.a54 t3.t2.t350 t3.t2.t359 t3.t2.t105 t3.t2.t360 t3.t2.t97 t3.t2.t98))
% 2.33/2.57  (step t3.t2.t362 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)) (tptp.and tptp.truth (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t72 t3.t2.t361))
% 2.33/2.57  (step t3.t2.t363 (cl (= (tptp.and tptp.truth (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) :rule symm :premises (t3.t2.t362))
% 2.33/2.57  (step t3.t2.t364 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)) (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x))) :rule symm :premises (t3.t2.a104))
% 2.33/2.57  (step t3.t2.t365 (cl (= (tptp.and tptp.truth tptp.x) (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x))) :rule cong :premises (t3.t2.t259 t3.t2.t44))
% 2.33/2.57  (step t3.t2.t366 (cl (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and tptp.truth tptp.x))) :rule symm :premises (t3.t2.t365))
% 2.33/2.57  (step t3.t2.t367 (cl (= (tptp.not (tptp.not tptp.falsehood)) tptp.falsehood)) :rule symm :premises (t3.t2.t346))
% 2.33/2.57  (step t3.t2.t368 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) tptp.falsehood))) :rule cong :premises (t3.t2.t85 t3.t2.t367))
% 2.33/2.57  (step t3.t2.t369 (cl (= (tptp.or (tptp.not tptp.x) tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.t368))
% 2.33/2.57  (step t3.t2.t370 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a106))
% 2.33/2.57  (step t3.t2.t371 (cl (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t78 t3.t2.t153))
% 2.33/2.57  (step t3.t2.t372 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t83))
% 2.33/2.57  (step t3.t2.t373 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.not tptp.truth))) :rule trans :premises (t3.t2.t76 t3.t2.t117 t3.t2.t118 t3.t2.t120 t3.t2.t133 t3.t2.t135 t3.t2.t127 t3.t2.t12 t3.t2.t38))
% 2.33/2.57  (step t3.t2.t374 (cl (= (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t372 t3.t2.t373))
% 2.33/2.57  (step t3.t2.t375 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule symm :premises (t3.t2.t374))
% 2.33/2.57  (step t3.t2.t376 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule trans :premises (t3.t2.t104 t3.t2.t375))
% 2.33/2.57  (step t3.t2.t377 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))) (tptp.and (tptp.not tptp.falsehood) tptp.x))) :rule symm :premises (t3.t2.a54))
% 2.33/2.57  (step t3.t2.t378 (cl (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) :rule symm :premises (t3.t2.t364))
% 2.33/2.57  (step t3.t2.t379 (cl (= (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))))) :rule trans :premises (t3.t2.t374 t3.t2.t103 t3.t2.a21 t3.t2.a103 t3.t2.t79 t3.t2.t80 t3.t2.t358 t3.t2.t349 t3.t2.t377 t3.t2.t340 t3.t2.t365 t3.t2.t378 t3.t2.t362 t3.t2.t338 t3.t2.t336))
% 2.33/2.57  (step t3.t2.t380 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.a107))
% 2.33/2.57  (step t3.t2.t381 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule symm :premises (t3.t2.t380))
% 2.33/2.57  (step t3.t2.t382 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.a105))
% 2.33/2.57  (step t3.t2.t383 (cl (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t382))
% 2.33/2.57  (step t3.t2.t384 (cl (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not (tptp.not tptp.x))))) :rule refl)
% 2.33/2.57  (step t3.t2.t385 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t154 t3.t2.t384))
% 2.33/2.57  (step t3.t2.t386 (cl (= (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t261 t3.t2.t384))
% 2.33/2.57  (step t3.t2.t387 (cl (= (tptp.implies (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t386))
% 2.33/2.57  (step t3.t2.t388 (cl (= (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.a122))
% 2.33/2.57  (step t3.t2.t389 (cl (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) tptp.truth))) :rule trans :premises (t3.t2.t383 t3.t2.t385 t3.t2.t387 t3.t2.t388 t3.t2.t83 t3.t2.t84))
% 2.33/2.57  (step t3.t2.t390 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule cong :premises (t3.t2.t389))
% 2.33/2.57  (step t3.t2.t391 (cl (= (tptp.not (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule cong :premises (t3.t2.t84))
% 2.33/2.57  (step t3.t2.t392 (cl (= (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.t391))
% 2.33/2.57  (step t3.t2.t393 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule trans :premises (t3.t2.t381 t3.t2.t390 t3.t2.t392))
% 2.33/2.57  (step t3.t2.t394 (cl (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not tptp.x) tptp.truth))) :rule trans :premises (t3.t2.t83 t3.t2.t84))
% 2.33/2.57  (step t3.t2.t395 (cl (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t394))
% 2.33/2.57  (step t3.t2.t396 (cl (= (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t395))
% 2.33/2.57  (step t3.t2.t397 (cl (= (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule trans :premises (t3.t2.t82 t3.t2.t376 t3.t2.t379 t3.t2.t393 t3.t2.t391 t3.t2.t396))
% 2.33/2.57  (step t3.t2.t398 (cl (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.a17))
% 2.33/2.57  (step t3.t2.t399 (cl (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule symm :premises (t3.t2.t398))
% 2.33/2.57  (step t3.t2.t400 (cl (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.and (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not tptp.x)))) :rule cong :premises (t3.t2.t82 t3.t2.t85))
% 2.33/2.57  (step t3.t2.t401 (cl (= (tptp.and tptp.truth tptp.x) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x))) :rule cong :premises (t3.t2.t114 t3.t2.t44))
% 2.33/2.57  (step t3.t2.t402 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x))) :rule trans :premises (t3.t2.a21 t3.t2.a103 t3.t2.t79 t3.t2.t80 t3.t2.t358 t3.t2.t349 t3.t2.t377 t3.t2.t340 t3.t2.t401))
% 2.33/2.57  (step t3.t2.t403 (cl (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not tptp.x)) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))) :rule cong :premises (t3.t2.t402 t3.t2.t85))
% 2.33/2.57  (step t3.t2.t404 (cl (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))))) :rule symm :premises (t3.t2.a110))
% 2.33/2.57  (step t3.t2.t405 (cl (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.t126))
% 2.33/2.57  (step t3.t2.t406 (cl (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth)))) (tptp.and tptp.falsehood (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.t125))
% 2.33/2.57  (step t3.t2.t407 (cl (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and tptp.falsehood (tptp.not tptp.falsehood)))) :rule trans :premises (t3.t2.t87 t3.t2.t89 t3.t2.t109 t3.t2.t110 t3.t2.t11 t3.t2.a70 t3.t2.t405 t3.t2.t406))
% 2.33/2.57  (step t3.t2.t408 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.falsehood (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t119 t3.t2.t407))
% 2.33/2.57  (step t3.t2.t409 (cl (= (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t113 t3.t2.t58 t3.t2.t191))
% 2.33/2.57  (step t3.t2.t410 (cl (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) :rule trans :premises (t3.t2.t125 t3.t2.t126 t3.t2.a53))
% 2.33/2.57  (step t3.t2.t411 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.falsehood (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) :rule cong :premises (t3.t2.t409 t3.t2.t410))
% 2.33/2.57  (step t3.t2.t412 (cl (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) :rule trans :premises (t3.t2.t399 t3.t2.t400 t3.t2.t403 t3.t2.t404 t3.t2.t408 t3.t2.t411 t3.t2.t197 t3.t2.t41 t3.t2.t12 t3.t2.t38))
% 2.33/2.57  (step t3.t2.t413 (cl (= (tptp.or (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.not tptp.truth) (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t295 t3.t2.t412))
% 2.33/2.57  (step t3.t2.t414 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not tptp.truth)) (tptp.or (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t413))
% 2.33/2.57  (step t3.t2.t415 (cl (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x))) :rule symm :premises (t3.t2.a2))
% 2.33/2.57  (step t3.t2.t416 (cl (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t415))
% 2.33/2.57  (step t3.t2.t417 (cl (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t416 t3.t2.t117 t3.t2.t118 t3.t2.t120 t3.t2.t133 t3.t2.t135 t3.t2.t127))
% 2.33/2.57  (step t3.t2.t418 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule symm :premises (t3.t2.t294))
% 2.33/2.57  (step t3.t2.t419 (cl (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule trans :premises (t3.t2.t415 t3.t2.t417 t3.t2.t418))
% 2.33/2.57  (step t3.t2.t420 (cl (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) :rule refl)
% 2.33/2.57  (step t3.t2.t421 (cl (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t419 t3.t2.t420))
% 2.33/2.57  (step t3.t2.t422 (cl (= (tptp.or (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t421))
% 2.33/2.57  (step t3.t2.t423 (cl (= (tptp.or (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x)) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule cong :premises (t3.t2.t398 t3.t2.t416))
% 2.33/2.57  (step t3.t2.t424 (cl (= (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x)))) :rule symm :premises (t3.t2.t423))
% 2.33/2.57  (step t3.t2.t425 (cl (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule refl)
% 2.33/2.57  (step t3.t2.t426 (cl (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t135))
% 2.33/2.57  (step t3.t2.t427 (cl (= (tptp.and (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t133))
% 2.33/2.57  (step t3.t2.t428 (cl (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t120))
% 2.33/2.57  (step t3.t2.t429 (cl (= (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t117))
% 2.33/2.57  (step t3.t2.t430 (cl (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x))) :rule trans :premises (t3.t2.t399 t3.t2.t400 t3.t2.t403 t3.t2.t404 t3.t2.t408 t3.t2.t411 t3.t2.t197 t3.t2.t41 t3.t2.a70 t3.t2.t426 t3.t2.t427 t3.t2.t428 t3.t2.a19 t3.t2.t429 t3.t2.t415))
% 2.33/2.57  (step t3.t2.t431 (cl (= (tptp.or (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x)))) :rule cong :premises (t3.t2.t425 t3.t2.t430))
% 2.33/2.57  (step t3.t2.t432 (cl (= (tptp.or (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x)) (tptp.or (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t431))
% 2.33/2.57  (step t3.t2.t433 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule symm :premises (t3.t2.a69))
% 2.33/2.57  (step t3.t2.t434 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) :rule trans :premises (t3.t2.t433 t3.t2.t398))
% 2.33/2.57  (step t3.t2.t435 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t433 t3.t2.t434))
% 2.33/2.57  (step t3.t2.t436 (cl (= (tptp.or (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))))) :rule symm :premises (t3.t2.t435))
% 2.33/2.57  (step t3.t2.t437 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))))) :rule trans :premises (t3.t2.t12 t3.t2.t38 t3.t2.t10 t3.t2.a45 t3.t2.t180 t3.t2.t188 t3.t2.t205 t3.t2.t210 t3.t2.t212 t3.t2.a9 t3.t2.t214 t3.t2.t414 t3.t2.t422 t3.t2.a81 t3.t2.t424 t3.t2.t432 t3.t2.t436))
% 2.33/2.57  (step t3.t2.t438 (cl (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))))) :rule cong :premises (t3.t2.t397 t3.t2.t437))
% 2.33/2.57  (step t3.t2.t439 (cl (= (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule refl)
% 2.33/2.57  (step t3.t2.t440 (cl (= (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.a81))
% 2.33/2.57  (step t3.t2.t441 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (tptp.not (tptp.not tptp.falsehood)))) :rule trans :premises (t3.t2.t435 t3.t2.t431 t3.t2.t423 t3.t2.t440 t3.t2.t421 t3.t2.t413 t3.t2.t213 t3.t2.t292 t3.t2.t211 t3.t2.t209 t3.t2.t204 t3.t2.t187 t3.t2.t179 t3.t2.t293 t3.t2.a47 t3.t2.t151 t3.t2.t64))
% 2.33/2.57  (step t3.t2.t442 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t439 t3.t2.t441))
% 2.33/2.57  (step t3.t2.t443 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a48))
% 2.33/2.57  (step t3.t2.t444 (cl (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a78))
% 2.33/2.57  (step t3.t2.t445 (cl (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t444))
% 2.33/2.57  (step t3.t2.t446 (cl (= (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not tptp.x))))) :rule trans :premises (t3.t2.t352 t3.t2.t353 t3.t2.t355 t3.t2.a65 t3.t2.t369 t3.t2.t370 t3.t2.t371 t3.t2.t438 t3.t2.t442 t3.t2.t443 t3.t2.t445 t3.t2.t383 t3.t2.t385 t3.t2.t387 t3.t2.t388))
% 2.33/2.57  (step t3.t2.t447 (cl (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.x))) :rule symm :premises (t3.t2.t446))
% 2.33/2.57  (step t3.t2.t448 (cl (= (tptp.not tptp.truth) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule symm :premises (t3.t2.t373))
% 2.33/2.57  (step t3.t2.t449 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.x) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule cong :premises (t3.t2.t447 t3.t2.t448))
% 2.33/2.57  (step t3.t2.t450 (cl (= (tptp.implies (tptp.not tptp.x) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (tptp.implies (tptp.not tptp.x) tptp.falsehood))) :rule cong :premises (t3.t2.t85 t3.t2.t137))
% 2.33/2.57  (step t3.t2.t451 (cl (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood))) :rule symm :premises (t3.t2.a1))
% 2.33/2.57  (step t3.t2.t452 (cl (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))) :rule symm :premises (t3.t2.t451))
% 2.33/2.57  (step t3.t2.t453 (cl (= (tptp.or tptp.falsehood tptp.x) (tptp.or tptp.x tptp.falsehood))) :rule symm :premises (t3.t2.a124))
% 2.33/2.57  (step t3.t2.t454 (cl (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) :rule symm :premises (t3.t2.t453))
% 2.33/2.57  (step t3.t2.t455 (cl (= (tptp.implies (tptp.not tptp.falsehood) tptp.x) (tptp.or tptp.falsehood tptp.x))) :rule symm :premises (t3.t2.a118))
% 2.33/2.57  (step t3.t2.t456 (cl (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) :rule symm :premises (t3.t2.t455))
% 2.33/2.57  (step t3.t2.t457 (cl (= (tptp.implies (tptp.not tptp.falsehood) tptp.x) (tptp.implies tptp.truth tptp.x))) :rule cong :premises (t3.t2.t72 t3.t2.t44))
% 2.33/2.57  (step t3.t2.t458 (cl (= (tptp.implies tptp.truth tptp.x) tptp.x)) :rule symm :premises (t3.t2.a32))
% 2.33/2.58  (step t3.t2.t459 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) tptp.x)) :rule trans :premises (t3.t2.t337 t3.t2.t339 t3.t2.t363 t3.t2.t364 t3.t2.t366 t3.t2.t341 t3.t2.a54 t3.t2.t350 t3.t2.t359 t3.t2.t105 t3.t2.t360 t3.t2.t97 t3.t2.t98 t3.t2.t104 t3.t2.t449 t3.t2.t450 t3.t2.t452 t3.t2.t454 t3.t2.t456 t3.t2.t457 t3.t2.t458))
% 2.33/2.58  (step t3.t2.t460 (cl (= tptp.x (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t459))
% 2.33/2.58  (step t3.t2.t461 (cl (= (tptp.not (tptp.not tptp.x)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))))) :rule trans :premises (t3.t2.t358 t3.t2.t349 t3.t2.t377 t3.t2.t340 t3.t2.t365 t3.t2.t378 t3.t2.t362 t3.t2.t338 t3.t2.t336))
% 2.33/2.58  (step t3.t2.t462 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))) :rule symm :premises (t3.t2.t461))
% 2.33/2.58  (step t3.t2.t463 (cl (= tptp.x (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t460 t3.t2.t462 t3.t2.t82))
% 2.33/2.58  (step t3.t2.t464 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood))) :rule cong :premises (t3.t2.t166 t3.t2.t39))
% 2.33/2.58  (step t3.t2.t465 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t464))
% 2.33/2.58  (step t3.t2.t466 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.a93))
% 2.33/2.58  (step t3.t2.t467 (cl (= (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.t144))
% 2.33/2.58  (step t3.t2.t468 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t143))
% 2.33/2.58  (step t3.t2.t469 (cl (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) :rule refl)
% 2.33/2.58  (step t3.t2.t470 (cl (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t346 t3.t2.t469))
% 2.33/2.58  (step t3.t2.t471 (cl (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a61))
% 2.33/2.58  (step t3.t2.t472 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.not (tptp.not tptp.falsehood)))) :rule trans :premises (t3.t2.t76 t3.t2.t117 t3.t2.t118 t3.t2.t120 t3.t2.t133 t3.t2.t135 t3.t2.t127 t3.t2.t12 t3.t2.t38 t3.t2.t151 t3.t2.t64))
% 2.33/2.58  (step t3.t2.t473 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t139 t3.t2.t472))
% 2.33/2.58  (step t3.t2.t474 (cl (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule symm :premises (t3.t2.t473))
% 2.33/2.58  (step t3.t2.t475 (cl (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule trans :premises (t3.t2.a55 t3.t2.t467 t3.t2.t468 t3.t2.a46 t3.t2.t470 t3.t2.t471 t3.t2.t474))
% 2.33/2.58  (step t3.t2.t476 (cl (= (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))))) :rule cong :premises (t3.t2.t475))
% 2.33/2.58  (step t3.t2.t477 (cl (= (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.t156))
% 2.33/2.58  (step t3.t2.t478 (cl (= (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))) :rule trans :premises (t3.t2.t149 t3.t2.t152 t3.t2.t477))
% 2.33/2.58  (step t3.t2.t479 (cl (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t53 t3.t2.t478))
% 2.33/2.58  (step t3.t2.t480 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) :rule trans :premises (t3.t2.t473 t3.t2.t479))
% 2.33/2.58  (step t3.t2.t481 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) :rule cong :premises (t3.t2.t480))
% 2.33/2.58  (step t3.t2.t482 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.a94))
% 2.33/2.58  (step t3.t2.t483 (cl (= (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) :rule symm :premises (t3.t2.t165))
% 2.33/2.58  (step t3.t2.t484 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule cong :premises (t3.t2.t166 t3.t2.t483))
% 2.33/2.58  (step t3.t2.t485 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth))) :rule cong :premises (t3.t2.t166 t3.t2.t72))
% 2.33/2.58  (step t3.t2.t486 (cl (= (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth))) :rule trans :premises (t3.t2.t476 t3.t2.t481 t3.t2.t482 t3.t2.t484 t3.t2.t485))
% 2.33/2.58  (step t3.t2.t487 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t486 t3.t2.a47))
% 2.33/2.58  (step t3.t2.t488 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood))) :rule symm :premises (t3.t2.t487))
% 2.33/2.58  (step t3.t2.t489 (cl (= (tptp.and tptp.falsehood tptp.x) (tptp.and tptp.x (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t3 t3.t2.t5 t3.t2.t49 t3.t2.t50))
% 2.33/2.58  (step t3.t2.t490 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.falsehood tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t73 t3.t2.t489))
% 2.33/2.58  (step t3.t2.t491 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.falsehood tptp.x)))) :rule symm :premises (t3.t2.t490))
% 2.33/2.58  (step t3.t2.t492 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.falsehood tptp.x)))) :rule cong :premises (t3.t2.t73 t3.t2.t325))
% 2.33/2.58  (step t3.t2.t493 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.falsehood tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.t492))
% 2.33/2.58  (step t3.t2.t494 (cl (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule trans :premises (t3.t2.a35 t3.t2.t491 t3.t2.t493))
% 2.33/2.58  (step t3.t2.t495 (cl (= (tptp.not (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t494))
% 2.33/2.58  (step t3.t2.t496 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.a35))
% 2.33/2.58  (step t3.t2.t497 (cl (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and tptp.x tptp.falsehood))) :rule symm :premises (t3.t2.t50))
% 2.33/2.58  (step t3.t2.t498 (cl (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule cong :premises (t3.t2.t497 t3.t2.t73))
% 2.33/2.58  (step t3.t2.t499 (cl (= (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.a0))
% 2.33/2.58  (step t3.t2.t500 (cl (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule symm :premises (t3.t2.t499))
% 2.33/2.58  (step t3.t2.t501 (cl (= (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood))) :rule symm :premises (t3.t2.a96))
% 2.33/2.58  (step t3.t2.t502 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t466))
% 2.33/2.58  (step t3.t2.t503 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.t333))
% 2.33/2.58  (step t3.t2.t504 (cl (= (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule trans :premises (t3.t2.t501 t3.t2.t487 t3.t2.t502 t3.t2.t464 t3.t2.t503))
% 2.33/2.58  (step t3.t2.t505 (cl (= (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and tptp.x (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.t44 t3.t2.t504))
% 2.33/2.58  (step t3.t2.t506 (cl (= (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a68))
% 2.33/2.58  (step t3.t2.t507 (cl (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.a98))
% 2.33/2.58  (step t3.t2.t508 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule trans :premises (t3.t2.t492 t3.t2.t490 t3.t2.t496 t3.t2.t498 t3.t2.t500 t3.t2.t505 t3.t2.t334 t3.t2.t331 t3.t2.t506 t3.t2.t327 t3.t2.t323 t3.t2.t507))
% 2.33/2.58  (step t3.t2.t509 (cl (= (tptp.not (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t508))
% 2.33/2.58  (step t3.t2.t510 (cl (= (tptp.not (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule trans :premises (t3.t2.t495 t3.t2.t509))
% 2.33/2.58  (step t3.t2.t511 (cl (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule cong :premises (t3.t2.t178 t3.t2.t510))
% 2.33/2.58  (step t3.t2.t512 (cl (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule symm :premises (t3.t2.a34))
% 2.33/2.58  (step t3.t2.t513 (cl (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) :rule symm :premises (t3.t2.t512))
% 2.33/2.58  (step t3.t2.t514 (cl (= (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule refl)
% 2.33/2.58  (step t3.t2.t515 (cl (= (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule refl)
% 2.33/2.58  (step t3.t2.t516 (cl (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.t39 t3.t2.t515))
% 2.33/2.58  (step t3.t2.t517 (cl (= (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.t516))
% 2.33/2.58  (step t3.t2.t518 (cl (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule symm :premises (t3.t2.t400))
% 2.33/2.58  (step t3.t2.t519 (cl (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) :rule trans :premises (t3.t2.t518 t3.t2.t398))
% 2.33/2.58  (step t3.t2.t520 (cl (= (tptp.not (tptp.and (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not tptp.x))) (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t519))
% 2.33/2.58  (step t3.t2.t521 (cl (= (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.and (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t520))
% 2.33/2.58  (step t3.t2.t522 (cl (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t399 t3.t2.t400 t3.t2.t403 t3.t2.t404 t3.t2.t408 t3.t2.t411 t3.t2.t197 t3.t2.t41))
% 2.33/2.58  (step t3.t2.t523 (cl (= (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t522))
% 2.33/2.58  (step t3.t2.t524 (cl (= (tptp.not (tptp.and (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not tptp.x))) tptp.truth)) :rule trans :premises (t3.t2.t520 t3.t2.t523 t3.t2.t56 t3.t2.t17 t3.t2.t69 t3.t2.t70))
% 2.33/2.58  (step t3.t2.t525 (cl (= (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) tptp.truth)) :rule trans :premises (t3.t2.t521 t3.t2.t524))
% 2.33/2.58  (step t3.t2.t526 (cl (= (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x))) :rule symm :premises (t3.t2.a11))
% 2.33/2.58  (step t3.t2.t527 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x))) :rule symm :premises (t3.t2.a126))
% 2.33/2.58  (step t3.t2.t528 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) :rule symm :premises (t3.t2.t527))
% 2.33/2.58  (step t3.t2.t529 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.t166 t3.t2.t6))
% 2.33/2.58  (step t3.t2.t530 (cl (= (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.a47 t3.t2.t515))
% 2.33/2.58  (step t3.t2.t531 (cl (= (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))) (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule trans :premises (t3.t2.t526 t3.t2.t528 t3.t2.t529 t3.t2.a98 t3.t2.t324 t3.t2.a50 t3.t2.t530))
% 2.33/2.58  (step t3.t2.t532 (cl (= (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t525 t3.t2.t531))
% 2.33/2.58  (step t3.t2.t533 (cl (= (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t532))
% 2.33/2.58  (step t3.t2.t534 (cl (= (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule refl)
% 2.33/2.58  (step t3.t2.t535 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) :rule symm :premises (t3.t2.t529))
% 2.33/2.58  (step t3.t2.t536 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) :rule trans :premises (t3.t2.t535 t3.t2.t527 t3.t2.a11))
% 2.33/2.58  (step t3.t2.t537 (cl (= (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t534 t3.t2.t536))
% 2.33/2.58  (step t3.t2.t538 (cl (= (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.t537))
% 2.33/2.58  (step t3.t2.t539 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) :rule symm :premises (t3.t2.a125))
% 2.33/2.58  (step t3.t2.t540 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) :rule symm :premises (t3.t2.t539))
% 2.33/2.58  (step t3.t2.t541 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.t166 t3.t2.t48))
% 2.33/2.58  (step t3.t2.t542 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule trans :premises (t3.t2.t540 t3.t2.t541))
% 2.33/2.58  (step t3.t2.t543 (cl (= (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t534 t3.t2.t542))
% 2.33/2.58  (step t3.t2.t544 (cl (= (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) :rule symm :premises (t3.t2.t543))
% 2.33/2.58  (step t3.t2.t545 (cl (= (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)) (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood))) :rule symm :premises (t3.t2.a123))
% 2.33/2.58  (step t3.t2.t546 (cl (= tptp.falsehood (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood))) :rule trans :premises (t3.t2.a47 t3.t2.t318 t3.t2.t321 t3.t2.t322 t3.t2.a98 t3.t2.t324 t3.t2.a50 t3.t2.t517 t3.t2.a40 t3.t2.t533 t3.t2.t538 t3.t2.t544 t3.t2.t545))
% 2.33/2.58  (step t3.t2.t547 (cl (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood)))) :rule cong :premises (t3.t2.t514 t3.t2.t546))
% 2.33/2.58  (step t3.t2.t548 (cl (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) :rule symm :premises (t3.t2.t545))
% 2.33/2.58  (step t3.t2.t549 (cl (= (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.a40))
% 2.33/2.58  (step t3.t2.t550 (cl (= (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a50))
% 2.33/2.58  (step t3.t2.t551 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) :rule symm :premises (t3.t2.t541))
% 2.33/2.58  (step t3.t2.t552 (cl (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) :rule trans :premises (t3.t2.t548 t3.t2.t543 t3.t2.t537 t3.t2.t532 t3.t2.t549 t3.t2.t516 t3.t2.t550 t3.t2.t323 t3.t2.t507 t3.t2.t551 t3.t2.t539))
% 2.33/2.58  (step t3.t2.t553 (cl (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood)) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) :rule cong :premises (t3.t2.t514 t3.t2.t552))
% 2.33/2.58  (step t3.t2.t554 (cl (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t514 t3.t2.t542))
% 2.33/2.58  (step t3.t2.t555 (cl (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule symm :premises (t3.t2.a63))
% 2.33/2.58  (step t3.t2.t556 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule symm :premises (t3.t2.t322))
% 2.33/2.58  (step t3.t2.t557 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.t309))
% 2.33/2.58  (step t3.t2.t558 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t557 t3.t2.t266))
% 2.33/2.58  (step t3.t2.t559 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule cong :premises (t3.t2.t558))
% 2.33/2.58  (step t3.t2.t560 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule symm :premises (t3.t2.t559))
% 2.33/2.58  (step t3.t2.t561 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule refl)
% 2.33/2.58  (step t3.t2.t562 (cl (= (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t266))
% 2.33/2.58  (step t3.t2.t563 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t267 t3.t2.t65))
% 2.33/2.58  (step t3.t2.t564 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t563))
% 2.33/2.58  (step t3.t2.t565 (cl (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t273 t3.t2.t281 t3.t2.t284 t3.t2.t285 t3.t2.a92 t3.t2.t564))
% 2.33/2.58  (step t3.t2.t566 (cl (= (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t565))
% 2.33/2.58  (step t3.t2.t567 (cl (= (tptp.or (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t266 t3.t2.t373))
% 2.33/2.58  (step t3.t2.t568 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule symm :premises (t3.t2.t567))
% 2.33/2.58  (step t3.t2.t569 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule trans :premises (t3.t2.t563 t3.t2.t568))
% 2.33/2.58  (step t3.t2.t570 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))))) :rule cong :premises (t3.t2.t569))
% 2.33/2.58  (step t3.t2.t571 (cl (= (tptp.not (tptp.or (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t567))
% 2.33/2.58  (step t3.t2.t572 (cl (= (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t562 t3.t2.t566 t3.t2.t570 t3.t2.t571 t3.t2.t138 t3.t2.a82 t3.t2.t8 t3.t2.t9 t3.t2.t46 t3.t2.t47 t3.t2.t3 t3.t2.t5 t3.t2.t49 t3.t2.t50))
% 2.33/2.58  (step t3.t2.t573 (cl (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t561 t3.t2.t572))
% 2.33/2.58  (step t3.t2.t574 (cl (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule symm :premises (t3.t2.t573))
% 2.33/2.58  (step t3.t2.t575 (cl (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule symm :premises (t3.t2.a95))
% 2.33/2.58  (step t3.t2.t576 (cl (= (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule refl)
% 2.33/2.58  (step t3.t2.t577 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule cong :premises (t3.t2.t309 t3.t2.t576))
% 2.33/2.58  (step t3.t2.t578 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule cong :premises (t3.t2.t577))
% 2.33/2.58  (step t3.t2.t579 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule symm :premises (t3.t2.t578))
% 2.33/2.58  (step t3.t2.t580 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule trans :premises (t3.t2.t556 t3.t2.t560 t3.t2.a86 t3.t2.t574 t3.t2.t575 t3.t2.t579))
% 2.33/2.58  (step t3.t2.t581 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule symm :premises (t3.t2.a24))
% 2.33/2.58  (step t3.t2.t582 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a83))
% 2.33/2.58  (step t3.t2.t583 (cl (= (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule symm :premises (t3.t2.a38))
% 2.33/2.58  (step t3.t2.t584 (cl (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.t583))
% 2.33/2.58  (step t3.t2.t585 (cl (= (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.t562))
% 2.33/2.58  (step t3.t2.t586 (cl (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t273 t3.t2.t281 t3.t2.t284 t3.t2.t285 t3.t2.a92))
% 2.33/2.58  (step t3.t2.t587 (cl (= (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t585 t3.t2.t586))
% 2.33/2.58  (step t3.t2.t588 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.a13))
% 2.33/2.58  (step t3.t2.t589 (cl (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) :rule symm :premises (t3.t2.t588))
% 2.33/2.58  (step t3.t2.t590 (cl (= (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule cong :premises (t3.t2.t576 t3.t2.t557))
% 2.33/2.58  (step t3.t2.t591 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t590))
% 2.33/2.58  (step t3.t2.t592 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a79))
% 2.33/2.58  (step t3.t2.t593 (cl (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule trans :premises (t3.t2.t584 t3.t2.t587 t3.t2.t589 t3.t2.t591 t3.t2.t592))
% 2.33/2.58  (step t3.t2.t594 (cl (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule symm :premises (t3.t2.t593))
% 2.33/2.58  (step t3.t2.t595 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule trans :premises (t3.t2.t580 t3.t2.t581 t3.t2.t582 t3.t2.t594))
% 2.33/2.58  (step t3.t2.t596 (cl (= (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule cong :premises (t3.t2.t580))
% 2.33/2.58  (step t3.t2.t597 (cl (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule symm :premises (t3.t2.t582))
% 2.33/2.58  (step t3.t2.t598 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule symm :premises (t3.t2.t581))
% 2.33/2.58  (step t3.t2.t599 (cl (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule trans :premises (t3.t2.t584 t3.t2.t587 t3.t2.t589 t3.t2.t591 t3.t2.t592 t3.t2.t597 t3.t2.t598))
% 2.33/2.58  (step t3.t2.t600 (cl (= (tptp.not (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (tptp.not (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule cong :premises (t3.t2.t599))
% 2.33/2.58  (step t3.t2.t601 (cl (= (tptp.not (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (tptp.not (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule symm :premises (t3.t2.t600))
% 2.33/2.58  (step t3.t2.t602 (cl (= (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule trans :premises (t3.t2.t596 t3.t2.t601))
% 2.33/2.58  (step t3.t2.t603 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))))) :rule cong :premises (t3.t2.t595 t3.t2.t602))
% 2.33/2.58  (step t3.t2.t604 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule symm :premises (t3.t2.t575))
% 2.33/2.58  (step t3.t2.t605 (cl (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule symm :premises (t3.t2.a86))
% 2.33/2.58  (step t3.t2.t606 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t578 t3.t2.t604 t3.t2.t573 t3.t2.t605 t3.t2.t559 t3.t2.t320 t3.t2.t317 t3.t2.t110 t3.t2.t11))
% 2.33/2.58  (step t3.t2.t607 (cl (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not tptp.truth))) :rule trans :premises (t3.t2.t593 t3.t2.t597 t3.t2.t598 t3.t2.t606 t3.t2.t39 t3.t2.a47))
% 2.33/2.58  (step t3.t2.t608 (cl (= (tptp.not (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t606))
% 2.33/2.58  (step t3.t2.t609 (cl (= (tptp.not (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) tptp.truth)) :rule trans :premises (t3.t2.t600 t3.t2.t608 t3.t2.t56 t3.t2.t17 t3.t2.t69 t3.t2.t70))
% 2.33/2.58  (step t3.t2.t610 (cl (= (tptp.and (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule cong :premises (t3.t2.t607 t3.t2.t609))
% 2.33/2.58  (step t3.t2.t611 (cl (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) tptp.falsehood)) :rule trans :premises (t3.t2.t511 t3.t2.t513 t3.t2.t547 t3.t2.t553 t3.t2.t554 t3.t2.t555 t3.t2.t603 t3.t2.t610 t3.t2.t127 t3.t2.t12 t3.t2.t38 t3.t2.t10))
% 2.33/2.58  (step t3.t2.t612 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood))) :rule cong :premises (t3.t2.t73 t3.t2.t611))
% 2.33/2.58  (step t3.t2.t613 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule symm :premises (t3.t2.t612))
% 2.33/2.58  (step t3.t2.t614 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.a92))
% 2.33/2.58  (step t3.t2.t615 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.t286))
% 2.33/2.58  (step t3.t2.t616 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) :rule trans :premises (t3.t2.t614 t3.t2.t615))
% 2.33/2.58  (step t3.t2.t617 (cl (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule symm :premises (t3.t2.t511))
% 2.33/2.58  (step t3.t2.t618 (cl (= (tptp.and (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule cong :premises (t3.t2.t616 t3.t2.t617))
% 2.33/2.58  (step t3.t2.t619 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule symm :premises (t3.t2.t618))
% 2.33/2.58  (step t3.t2.t620 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule trans :premises (t3.t2.t333 t3.t2.t465 t3.t2.t466 t3.t2.t488 t3.t2.t613 t3.t2.t619))
% 2.33/2.58  (step t3.t2.t621 (cl (= (tptp.and tptp.x (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (tptp.and (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))))) :rule cong :premises (t3.t2.t463 t3.t2.t620))
% 2.33/2.58  (step t3.t2.t622 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) tptp.x)) :rule symm :premises (t3.t2.t463))
% 2.33/2.58  (step t3.t2.t623 (cl (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (tptp.and tptp.x (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule cong :premises (t3.t2.t622 t3.t2.t618))
% 2.33/2.58  (step t3.t2.t624 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.a77))
% 2.33/2.58  (step t3.t2.t625 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t3.t2.t624))
% 2.33/2.58  (step t3.t2.t626 (cl (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.t624))
% 2.33/2.58  (step t3.t2.t627 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule refl)
% 2.33/2.58  (step t3.t2.t628 (cl (= (tptp.and (tptp.not tptp.truth) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule cong :premises (t3.t2.t10 t3.t2.t514))
% 2.33/2.58  (step t3.t2.t629 (cl (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not tptp.truth) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule symm :premises (t3.t2.t628))
% 2.33/2.58  (step t3.t2.t630 (cl (= (tptp.not (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (tptp.not (tptp.and (tptp.not tptp.truth) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule cong :premises (t3.t2.t629))
% 2.33/2.58  (step t3.t2.t631 (cl (= (tptp.and (tptp.not tptp.truth) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule trans :premises (t3.t2.t628 t3.t2.t513 t3.t2.t547 t3.t2.t553 t3.t2.t554 t3.t2.t555))
% 2.33/2.58  (step t3.t2.t632 (cl (= (tptp.not (tptp.and (tptp.not tptp.truth) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (tptp.not (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule cong :premises (t3.t2.t631))
% 2.33/2.58  (step t3.t2.t633 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule trans :premises (t3.t2.t582 t3.t2.t594))
% 2.33/2.58  (step t3.t2.t634 (cl (= (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (tptp.not (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule cong :premises (t3.t2.t598))
% 2.33/2.58  (step t3.t2.t635 (cl (= (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (tptp.not (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule trans :premises (t3.t2.t634 t3.t2.t601))
% 2.33/2.58  (step t3.t2.t636 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))))) :rule cong :premises (t3.t2.t633 t3.t2.t635))
% 2.33/2.58  (step t3.t2.t637 (cl (= (tptp.and (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.not (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule symm :premises (t3.t2.t636))
% 2.33/2.58  (step t3.t2.t638 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule trans :premises (t3.t2.t603 t3.t2.t637))
% 2.33/2.58  (step t3.t2.t639 (cl (= (tptp.not (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (tptp.not (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule cong :premises (t3.t2.t638))
% 2.33/2.58  (step t3.t2.t640 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t636 t3.t2.t610 t3.t2.t127))
% 2.33/2.58  (step t3.t2.t641 (cl (= (tptp.not (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t640))
% 2.33/2.58  (step t3.t2.t642 (cl (= (tptp.not (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (tptp.not tptp.falsehood))) :rule trans :premises (t3.t2.t630 t3.t2.t632 t3.t2.t639 t3.t2.t641 t3.t2.t56))
% 2.33/2.58  (step t3.t2.t643 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) :rule cong :premises (t3.t2.t627 t3.t2.t642))
% 2.33/2.58  (step t3.t2.t644 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))))) :rule symm :premises (t3.t2.t643))
% 2.33/2.58  (step t3.t2.t645 (cl (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))))) :rule trans :premises (t3.t2.t626 t3.t2.t644))
% 2.33/2.58  (step t3.t2.t646 (cl (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))))) :rule cong :premises (t3.t2.t645))
% 2.33/2.58  (step t3.t2.t647 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.a39))
% 2.33/2.58  (step t3.t2.t648 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.t647))
% 2.33/2.58  (step t3.t2.t649 (cl (= (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (tptp.implies (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t557 t3.t2.t373))
% 2.33/2.58  (step t3.t2.t650 (cl (= (tptp.implies (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule symm :premises (t3.t2.t649))
% 2.33/2.58  (step t3.t2.t651 (cl (= (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule trans :premises (t3.t2.t266 t3.t2.t273 t3.t2.t281 t3.t2.t284 t3.t2.t285 t3.t2.a92 t3.t2.t297 t3.t2.t298 t3.t2.t303 t3.t2.a80 t3.t2.t311 t3.t2.t650))
% 2.33/2.58  (step t3.t2.t652 (cl (= (tptp.implies (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t284 t3.t2.t285 t3.t2.a92 t3.t2.t297 t3.t2.t298 t3.t2.t303 t3.t2.a80 t3.t2.t311))
% 2.33/2.58  (step t3.t2.t653 (cl (= (tptp.implies (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.truth)) (tptp.implies (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.t652))
% 2.33/2.58  (step t3.t2.t654 (cl (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule trans :premises (t3.t2.t265 t3.t2.t651 t3.t2.t649 t3.t2.t653))
% 2.33/2.58  (step t3.t2.t655 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))) tptp.truth)) :rule symm :premises (t3.t2.a114))
% 2.33/2.58  (step t3.t2.t656 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule symm :premises (t3.t2.t655))
% 2.33/2.58  (step t3.t2.t657 (cl (= (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule refl)
% 2.33/2.58  (step t3.t2.t658 (cl (= (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t657 t3.t2.t52))
% 2.33/2.58  (step t3.t2.t659 (cl (= (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule symm :premises (t3.t2.a90))
% 2.33/2.58  (step t3.t2.t660 (cl (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule symm :premises (t3.t2.a119))
% 2.33/2.58  (step t3.t2.t661 (cl (= (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule symm :premises (t3.t2.a56))
% 2.33/2.58  (step t3.t2.t662 (cl (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule symm :premises (t3.t2.t661))
% 2.33/2.58  (step t3.t2.t663 (cl (= (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule cong :premises (t3.t2.t73 t3.t2.t84))
% 2.33/2.58  (step t3.t2.t664 (cl (= (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.t663))
% 2.33/2.58  (step t3.t2.t665 (cl (= (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule trans :premises (t3.t2.t658 t3.t2.t659 t3.t2.t660 t3.t2.t662 t3.t2.t664))
% 2.33/2.58  (step t3.t2.t666 (cl (= (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule trans :premises (t3.t2.t665 t3.t2.t663))
% 2.33/2.58  (step t3.t2.t667 (cl (= (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule refl)
% 2.33/2.58  (step t3.t2.t668 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule cong :premises (t3.t2.t666 t3.t2.t667))
% 2.33/2.58  (step t3.t2.t669 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule cong :premises (t3.t2.t52 t3.t2.t84))
% 2.33/2.58  (step t3.t2.t670 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule trans :premises (t3.t2.t669 t3.t2.t662 t3.t2.t664))
% 2.33/2.58  (step t3.t2.t671 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule trans :premises (t3.t2.t670 t3.t2.t663))
% 2.33/2.58  (step t3.t2.t672 (cl (= (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.t671))
% 2.33/2.58  (step t3.t2.t673 (cl (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) :rule cong :premises (t3.t2.t78 t3.t2.t72))
% 2.33/2.58  (step t3.t2.t674 (cl (= (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth) (tptp.or (tptp.not tptp.x) tptp.truth))) :rule symm :premises (t3.t2.a4))
% 2.33/2.58  (step t3.t2.t675 (cl (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.or tptp.truth (tptp.not tptp.x)))) :rule symm :premises (t3.t2.a62))
% 2.33/2.58  (step t3.t2.t676 (cl (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)))) :rule symm :premises (t3.t2.a28))
% 2.33/2.58  (step t3.t2.t677 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)))) :rule trans :premises (t3.t2.t275 t3.t2.t673 t3.t2.t674 t3.t2.t675 t3.t2.t676))
% 2.33/2.58  (step t3.t2.t678 (cl (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.implies tptp.falsehood (tptp.not tptp.x)))) :rule cong :premises (t3.t2.t10 t3.t2.t85))
% 2.33/2.58  (step t3.t2.t679 (cl (= tptp.falsehood (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule symm :premises (t3.t2.t137))
% 2.33/2.58  (step t3.t2.t680 (cl (= (tptp.implies tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.not tptp.x)))) :rule cong :premises (t3.t2.t679 t3.t2.t85))
% 2.33/2.58  (step t3.t2.t681 (cl (= (tptp.implies (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.not tptp.x)) (tptp.implies tptp.falsehood (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t137 t3.t2.t446))
% 2.33/2.58  (step t3.t2.t682 (cl (= (tptp.implies tptp.falsehood (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t346 t3.t2.t384))
% 2.33/2.58  (step t3.t2.t683 (cl (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule trans :premises (t3.t2.t678 t3.t2.t680 t3.t2.t681 t3.t2.t682))
% 2.33/2.58  (step t3.t2.t684 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule trans :premises (t3.t2.t677 t3.t2.t683))
% 2.33/2.58  (step t3.t2.t685 (cl (= (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t684 t3.t2.t395))
% 2.33/2.58  (step t3.t2.t686 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) :rule symm :premises (t3.t2.a16))
% 2.33/2.58  (step t3.t2.t687 (cl (= (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth))) :rule trans :premises (t3.t2.t149 t3.t2.t152))
% 2.33/2.58  (step t3.t2.t688 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t384 t3.t2.t687))
% 2.33/2.58  (step t3.t2.t689 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t688 t3.t2.t103))
% 2.33/2.58  (step t3.t2.t690 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.x)))) :rule trans :premises (t3.t2.t689 t3.t2.t81))
% 2.33/2.58  (step t3.t2.t691 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule cong :premises (t3.t2.t690 t3.t2.t153))
% 2.33/2.58  (step t3.t2.t692 (cl (= (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.not (tptp.not tptp.x))))) :rule trans :premises (t3.t2.t685 t3.t2.t686 t3.t2.t691 t3.t2.t438 t3.t2.t442 t3.t2.t443 t3.t2.t445 t3.t2.t383 t3.t2.t385 t3.t2.t387 t3.t2.t388))
% 2.33/2.58  (step t3.t2.t693 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))) (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t672 t3.t2.t692))
% 2.33/2.58  (step t3.t2.t694 (cl (= (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule cong :premises (t3.t2.t73 t3.t2.t83))
% 2.33/2.58  (step t3.t2.t695 (cl (= (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule symm :premises (t3.t2.t670))
% 2.33/2.58  (step t3.t2.t696 (cl (= (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule trans :premises (t3.t2.t694 t3.t2.t695))
% 2.33/2.58  (step t3.t2.t697 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t696 t3.t2.t384))
% 2.33/2.58  (step t3.t2.t698 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t697))
% 2.33/2.58  (step t3.t2.t699 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule refl)
% 2.33/2.58  (step t3.t2.t700 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule cong :premises (t3.t2.t699 t3.t2.t265))
% 2.33/2.58  (step t3.t2.t701 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.t700))
% 2.33/2.58  (step t3.t2.t702 (cl (= (tptp.not tptp.falsehood) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule trans :premises (t3.t2.t17 t3.t2.t69 t3.t2.t70 t3.t2.t656 t3.t2.t668 t3.t2.t693 t3.t2.t698 t3.t2.a85 t3.t2.t701))
% 2.33/2.58  (step t3.t2.t703 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule cong :premises (t3.t2.t654 t3.t2.t702))
% 2.33/2.58  (step t3.t2.t704 (cl (= (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule refl)
% 2.33/2.58  (step t3.t2.t705 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) :rule symm :premises (t3.t2.a66))
% 2.33/2.58  (step t3.t2.t706 (cl (= (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.not tptp.truth))) :rule trans :premises (t3.t2.t705 t3.t2.t399 t3.t2.t400 t3.t2.t403 t3.t2.t404 t3.t2.t408 t3.t2.t411 t3.t2.t197 t3.t2.t41 t3.t2.t12 t3.t2.t38))
% 2.33/2.58  (step t3.t2.t707 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) :rule cong :premises (t3.t2.t704 t3.t2.t706))
% 2.33/2.58  (step t3.t2.t708 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.a89))
% 2.33/2.58  (step t3.t2.t709 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.implies (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t707 t3.t2.t708 t3.t2.t297 t3.t2.t298 t3.t2.t303 t3.t2.a80 t3.t2.t311))
% 2.33/2.58  (step t3.t2.t710 (cl (= (tptp.implies (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule symm :premises (t3.t2.t709))
% 2.33/2.58  (step t3.t2.t711 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule symm :premises (t3.t2.t707))
% 2.33/2.58  (step t3.t2.t712 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule trans :premises (t3.t2.a89 t3.t2.t711))
% 2.33/2.58  (step t3.t2.t713 (cl (= (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.t712))
% 2.33/2.58  (step t3.t2.t714 (cl (= (tptp.implies (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t652 t3.t2.t710 t3.t2.t713))
% 2.33/2.58  (step t3.t2.t715 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.a85))
% 2.33/2.58  (step t3.t2.t716 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule symm :premises (t3.t2.t693))
% 2.33/2.58  (step t3.t2.t717 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))) (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule symm :premises (t3.t2.t668))
% 2.33/2.58  (step t3.t2.t718 (cl (= (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule symm :premises (t3.t2.t396))
% 2.33/2.58  (step t3.t2.t719 (cl (= (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule symm :premises (t3.t2.t390))
% 2.33/2.58  (step t3.t2.t720 (cl (= (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) :rule trans :premises (t3.t2.t718 t3.t2.t719 t3.t2.t380 t3.t2.t337 t3.t2.t339 t3.t2.t363 t3.t2.t364 t3.t2.t366 t3.t2.t341 t3.t2.a54 t3.t2.t350 t3.t2.t359 t3.t2.t105))
% 2.33/2.58  (step t3.t2.t721 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule cong :premises (t3.t2.t104 t3.t2.t720))
% 2.33/2.58  (step t3.t2.t722 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule symm :premises (t3.t2.t721))
% 2.33/2.58  (step t3.t2.t723 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth))) (tptp.implies (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule cong :premises (t3.t2.t93 t3.t2.t396))
% 2.33/2.58  (step t3.t2.t724 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule symm :premises (t3.t2.t723))
% 2.33/2.58  (step t3.t2.t725 (cl (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule cong :premises (t3.t2.t82 t3.t2.t718))
% 2.33/2.58  (step t3.t2.t726 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule symm :premises (t3.t2.t725))
% 2.33/2.58  (step t3.t2.t727 (cl (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule symm :premises (t3.t2.a116))
% 2.33/2.58  (step t3.t2.t728 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule trans :premises (t3.t2.t700 t3.t2.t715 t3.t2.t697 t3.t2.t716 t3.t2.t717 t3.t2.t655 t3.t2.a10 t3.t2.t722 t3.t2.t724 t3.t2.t726 t3.t2.t727))
% 2.33/2.58  (step t3.t2.t729 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.implies (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule cong :premises (t3.t2.t714 t3.t2.t728))
% 2.33/2.58  (step t3.t2.t730 (cl (= (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)) (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)))) :rule symm :premises (t3.t2.a80))
% 2.33/2.58  (step t3.t2.t731 (cl (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule symm :premises (t3.t2.t298))
% 2.33/2.58  (step t3.t2.t732 (cl (= (tptp.implies (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule trans :premises (t3.t2.t310 t3.t2.t730 t3.t2.t302 t3.t2.t731 t3.t2.t296 t3.t2.t614 t3.t2.t288 t3.t2.t283 t3.t2.t290))
% 2.33/2.58  (step t3.t2.t733 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule trans :premises (t3.t2.t712 t3.t2.t709 t3.t2.t732))
% 2.33/2.58  (step t3.t2.t734 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule symm :premises (t3.t2.t727))
% 2.33/2.58  (step t3.t2.t735 (cl (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule symm :premises (t3.t2.t388))
% 2.33/2.58  (step t3.t2.t736 (cl (= (tptp.implies (tptp.not (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule cong :premises (t3.t2.t56 t3.t2.t394))
% 2.33/2.58  (step t3.t2.t737 (cl (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule trans :premises (t3.t2.t735 t3.t2.t386 t3.t2.t736))
% 2.33/2.58  (step t3.t2.t738 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule cong :premises (t3.t2.t671 t3.t2.t737))
% 2.33/2.58  (step t3.t2.t739 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule trans :premises (t3.t2.t734 t3.t2.t725 t3.t2.t723 t3.t2.t721 t3.t2.t107 t3.t2.t656 t3.t2.t668 t3.t2.t693 t3.t2.t738))
% 2.33/2.58  (step t3.t2.t740 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule cong :premises (t3.t2.t733 t3.t2.t739))
% 2.33/2.58  (step t3.t2.t741 (cl (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))) tptp.truth)) :rule symm :premises (t3.t2.a58))
% 2.33/2.58  (step t3.t2.t742 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) tptp.truth)) :rule trans :premises (t3.t2.t643 t3.t2.t648 t3.t2.t703 t3.t2.t729 t3.t2.t740 t3.t2.t741))
% 2.33/2.58  (step t3.t2.t743 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) (tptp.not tptp.truth))) :rule cong :premises (t3.t2.t742))
% 2.33/2.58  (step t3.t2.t744 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.not (tptp.not tptp.falsehood)))) :rule trans :premises (t3.t2.t612 t3.t2.t487 t3.t2.t502 t3.t2.t464 t3.t2.t503 t3.t2.t625 t3.t2.t646 t3.t2.t743 t3.t2.t151 t3.t2.t64))
% 2.33/2.58  (step t3.t2.t745 (cl (= (tptp.and tptp.x (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (tptp.and (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))))) :rule cong :premises (t3.t2.t463 t3.t2.t744))
% 2.33/2.58  (step t3.t2.t746 (cl (= (tptp.and tptp.x tptp.truth) (tptp.and tptp.x (tptp.not tptp.falsehood)))) :rule cong :premises (t3.t2.t44 t3.t2.t75))
% 2.33/2.58  (step t3.t2.t747 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (tptp.and tptp.x (tptp.not tptp.falsehood)))) :rule symm :premises (t3.t2.a102))
% 2.33/2.58  (step t3.t2.t748 (cl (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) :rule symm :premises (t3.t2.t747))
% 2.33/2.58  (step t3.t2.t749 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))) (tptp.or (tptp.not tptp.x) tptp.falsehood))) :rule cong :premises (t3.t2.t85 t3.t2.t157))
% 2.33/2.58  (step t3.t2.t750 (cl (= (tptp.or (tptp.not tptp.x) tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) :rule symm :premises (t3.t2.t749))
% 2.33/2.58  (step t3.t2.t751 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) :rule trans :premises (t3.t2.t368 t3.t2.t750))
% 2.33/2.58  (step t3.t2.t752 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) :rule cong :premises (t3.t2.t751))
% 2.33/2.58  (step t3.t2.t753 (cl (= (tptp.or (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.falsehood (tptp.not tptp.x)))) :rule symm :premises (t3.t2.a65))
% 2.33/2.58  (step t3.t2.t754 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))) (tptp.or (tptp.not tptp.truth) (tptp.not tptp.x)))) :rule trans :premises (t3.t2.t749 t3.t2.t753 t3.t2.t356))
% 2.33/2.58  (step t3.t2.t755 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not tptp.x))))) :rule cong :premises (t3.t2.t754))
% 2.33/2.58  (step t3.t2.t756 (cl (= (tptp.and tptp.x tptp.truth) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x))) :rule trans :premises (t3.t2.t746 t3.t2.t748 t3.t2.t752 t3.t2.t755 t3.t2.t349 t3.t2.t377 t3.t2.t340 t3.t2.t401))
% 2.33/2.58  (step t3.t2.t757 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x tptp.truth))) :rule symm :premises (t3.t2.t756))
% 2.33/2.58  (step t3.t2.t758 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.and tptp.x tptp.truth))) :rule trans :premises (t3.t2.t402 t3.t2.t757))
% 2.33/2.58  (step t3.t2.t759 (cl (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.and tptp.x tptp.truth) tptp.falsehood))) :rule cong :premises (t3.t2.t758 t3.t2.t367))
% 2.33/2.58  (step t3.t2.t760 (cl (= (tptp.not tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule symm :premises (t3.t2.t109))
% 2.33/2.58  (step t3.t2.t761 (cl (= tptp.falsehood (tptp.and (tptp.not tptp.x) tptp.x))) :rule trans :premises (t3.t2.a47 t3.t2.t760 t3.t2.t88))
% 2.33/2.58  (step t3.t2.t762 (cl (= (tptp.and (tptp.and tptp.x tptp.truth) tptp.falsehood) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule cong :premises (t3.t2.t756 t3.t2.t761))
% 2.33/2.58  (step t3.t2.t763 (cl (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)) (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x))) :rule symm :premises (t3.t2.a109))
% 2.33/2.58  (step t3.t2.t764 (cl (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and tptp.truth (tptp.not tptp.truth)))) :rule trans :premises (t3.t2.t404 t3.t2.t408 t3.t2.t411 t3.t2.t197 t3.t2.t41))
% 2.33/2.58  (step t3.t2.t765 (cl (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.not tptp.truth))) :rule trans :premises (t3.t2.t764 t3.t2.t39 t3.t2.a47))
% 2.33/2.58  (step t3.t2.t766 (cl (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.not tptp.truth) tptp.x))) :rule cong :premises (t3.t2.t765 t3.t2.t44))
% 2.33/2.58  (step t3.t2.t767 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and_star tptp.x tptp.falsehood))) :rule symm :premises (t3.t2.a36))
% 2.33/2.58  (step t3.t2.t768 (cl (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule trans :premises (t3.t2.a47 t3.t2.t318 t3.t2.t321 t3.t2.t322 t3.t2.a98 t3.t2.t324 t3.t2.t328 t3.t2.a68 t3.t2.t332 t3.t2.t335 t3.t2.t621 t3.t2.t623 t3.t2.t745 t3.t2.t759 t3.t2.t762 t3.t2.t763 t3.t2.t766 t3.t2.t47 t3.t2.t3 t3.t2.t5 t3.t2.t767))
% 2.33/2.58  (step t3.t2 (cl (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) (not (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) (not (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) (not (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) (not (= tptp.x (tptp.implies tptp.truth tptp.x))) (not (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) (not (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) (not (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= tptp.falsehood (tptp.not tptp.truth))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) (not (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) (not (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (not (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) (not (= tptp.truth (tptp.implies tptp.truth tptp.truth))) (not (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) (not (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) (not (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) (not (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (not (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) (not (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) (not (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) (not (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) (not (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule subproof :discharge (t3.t2.a0 t3.t2.a1 t3.t2.a2 t3.t2.a3 t3.t2.a4 t3.t2.a5 t3.t2.a6 t3.t2.a7 t3.t2.a8 t3.t2.a9 t3.t2.a10 t3.t2.a11 t3.t2.a12 t3.t2.a13 t3.t2.a14 t3.t2.a15 t3.t2.a16 t3.t2.a17 t3.t2.a18 t3.t2.a19 t3.t2.a20 t3.t2.a21 t3.t2.a22 t3.t2.a23 t3.t2.a24 t3.t2.a25 t3.t2.a26 t3.t2.a27 t3.t2.a28 t3.t2.a29 t3.t2.a30 t3.t2.a31 t3.t2.a32 t3.t2.a33 t3.t2.a34 t3.t2.a35 t3.t2.a36 t3.t2.a37 t3.t2.a38 t3.t2.a39 t3.t2.a40 t3.t2.a41 t3.t2.a42 t3.t2.a43 t3.t2.a44 t3.t2.a45 t3.t2.a46 t3.t2.a47 t3.t2.a48 t3.t2.a49 t3.t2.a50 t3.t2.a51 t3.t2.a52 t3.t2.a53 t3.t2.a54 t3.t2.a55 t3.t2.a56 t3.t2.a57 t3.t2.a58 t3.t2.a59 t3.t2.a60 t3.t2.a61 t3.t2.a62 t3.t2.a63 t3.t2.a64 t3.t2.a65 t3.t2.a66 t3.t2.a67 t3.t2.a68 t3.t2.a69 t3.t2.a70 t3.t2.a71 t3.t2.a72 t3.t2.a73 t3.t2.a74 t3.t2.a75 t3.t2.a76 t3.t2.a77 t3.t2.a78 t3.t2.a79 t3.t2.a80 t3.t2.a81 t3.t2.a82 t3.t2.a83 t3.t2.a84 t3.t2.a85 t3.t2.a86 t3.t2.a87 t3.t2.a88 t3.t2.a89 t3.t2.a90 t3.t2.a91 t3.t2.a92 t3.t2.a93 t3.t2.a94 t3.t2.a95 t3.t2.a96 t3.t2.a97 t3.t2.a98 t3.t2.a99 t3.t2.a100 t3.t2.a101 t3.t2.a102 t3.t2.a103 t3.t2.a104 t3.t2.a105 t3.t2.a106 t3.t2.a107 t3.t2.a108 t3.t2.a109 t3.t2.a110 t3.t2.a111 t3.t2.a112 t3.t2.a113 t3.t2.a114 t3.t2.a115 t3.t2.a116 t3.t2.a117 t3.t2.a118 t3.t2.a119 t3.t2.a120 t3.t2.a121 t3.t2.a122 t3.t2.a123 t3.t2.a124 t3.t2.a125 t3.t2.a126 t3.t2.a127))
% 2.33/2.58  (step t3.t3 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule and_pos)
% 2.33/2.58  (step t3.t4 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))) :rule and_pos)
% 2.33/2.58  (step t3.t5 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.33/2.58  (step t3.t6 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.33/2.58  (step t3.t7 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) :rule and_pos)
% 2.33/2.58  (step t3.t8 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.58  (step t3.t9 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) :rule and_pos)
% 2.33/2.58  (step t3.t10 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))) :rule and_pos)
% 2.33/2.58  (step t3.t11 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.58  (step t3.t12 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))) :rule and_pos)
% 2.33/2.58  (step t3.t13 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.33/2.58  (step t3.t14 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) :rule and_pos)
% 2.33/2.58  (step t3.t15 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule and_pos)
% 2.33/2.58  (step t3.t16 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) :rule and_pos)
% 2.33/2.58  (step t3.t17 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.58  (step t3.t18 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule and_pos)
% 2.33/2.58  (step t3.t19 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.33/2.58  (step t3.t20 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule and_pos)
% 2.33/2.58  (step t3.t21 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.33/2.58  (step t3.t22 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) :rule and_pos)
% 2.33/2.58  (step t3.t23 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule and_pos)
% 2.33/2.58  (step t3.t24 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) :rule and_pos)
% 2.33/2.58  (step t3.t25 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.58  (step t3.t26 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule and_pos)
% 2.33/2.58  (step t3.t27 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule and_pos)
% 2.33/2.58  (step t3.t28 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule and_pos)
% 2.33/2.58  (step t3.t29 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule and_pos)
% 2.33/2.58  (step t3.t30 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.33/2.58  (step t3.t31 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x)))) :rule and_pos)
% 2.33/2.58  (step t3.t32 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.58  (step t3.t33 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.33/2.58  (step t3.t34 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.33/2.58  (step t3.t35 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.x (tptp.implies tptp.truth tptp.x))) :rule and_pos)
% 2.33/2.58  (step t3.t36 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule and_pos)
% 2.33/2.58  (step t3.t37 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) :rule and_pos)
% 2.33/2.58  (step t3.t38 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.33/2.58  (step t3.t39 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.58  (step t3.t40 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.33/2.58  (step t3.t41 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.33/2.58  (step t3.t42 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.33/2.58  (step t3.t43 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.33/2.58  (step t3.t44 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))) :rule and_pos)
% 2.33/2.58  (step t3.t45 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.33/2.58  (step t3.t46 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.33/2.58  (step t3.t47 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.58  (step t3.t48 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) :rule and_pos)
% 2.33/2.58  (step t3.t49 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.33/2.58  (step t3.t50 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.falsehood (tptp.not tptp.truth))) :rule and_pos)
% 2.33/2.58  (step t3.t51 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.58  (step t3.t52 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule and_pos)
% 2.33/2.58  (step t3.t53 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.33/2.58  (step t3.t54 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) :rule and_pos)
% 2.33/2.58  (step t3.t55 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.33/2.58  (step t3.t56 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) :rule and_pos)
% 2.33/2.58  (step t3.t57 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) :rule and_pos)
% 2.33/2.58  (step t3.t58 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.33/2.58  (step t3.t59 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule and_pos)
% 2.33/2.58  (step t3.t60 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) :rule and_pos)
% 2.33/2.58  (step t3.t61 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule and_pos)
% 2.33/2.59  (step t3.t62 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) :rule and_pos)
% 2.33/2.59  (step t3.t63 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.59  (step t3.t64 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.33/2.59  (step t3.t65 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) :rule and_pos)
% 2.33/2.59  (step t3.t66 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.33/2.59  (step t3.t67 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.33/2.59  (step t3.t68 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) :rule and_pos)
% 2.33/2.59  (step t3.t69 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule and_pos)
% 2.33/2.59  (step t3.t70 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule and_pos)
% 2.33/2.59  (step t3.t71 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.33/2.59  (step t3.t72 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.33/2.59  (step t3.t73 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule and_pos)
% 2.33/2.59  (step t3.t74 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.59  (step t3.t75 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule and_pos)
% 2.33/2.59  (step t3.t76 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) :rule and_pos)
% 2.33/2.59  (step t3.t77 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies tptp.truth tptp.truth))) :rule and_pos)
% 2.33/2.59  (step t3.t78 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x))) :rule and_pos)
% 2.33/2.59  (step t3.t79 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) :rule and_pos)
% 2.33/2.59  (step t3.t80 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.33/2.59  (step t3.t81 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.33/2.59  (step t3.t82 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.33/2.59  (step t3.t83 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule and_pos)
% 2.33/2.59  (step t3.t84 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule and_pos)
% 2.33/2.59  (step t3.t85 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.33/2.59  (step t3.t86 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule and_pos)
% 2.33/2.59  (step t3.t87 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule and_pos)
% 2.33/2.59  (step t3.t88 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule and_pos)
% 2.33/2.59  (step t3.t89 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.33/2.59  (step t3.t90 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) :rule and_pos)
% 2.33/2.59  (step t3.t91 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.33/2.59  (step t3.t92 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) :rule and_pos)
% 2.33/2.59  (step t3.t93 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.33/2.59  (step t3.t94 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) :rule and_pos)
% 2.33/2.59  (step t3.t95 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule and_pos)
% 2.33/2.59  (step t3.t96 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule and_pos)
% 2.33/2.59  (step t3.t97 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) :rule and_pos)
% 2.33/2.59  (step t3.t98 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule and_pos)
% 2.33/2.59  (step t3.t99 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule and_pos)
% 2.33/2.59  (step t3.t100 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.33/2.59  (step t3.t101 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.59  (step t3.t102 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule and_pos)
% 2.33/2.59  (step t3.t103 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) :rule and_pos)
% 2.33/2.59  (step t3.t104 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) :rule and_pos)
% 2.33/2.59  (step t3.t105 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.33/2.59  (step t3.t106 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) :rule and_pos)
% 2.33/2.59  (step t3.t107 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) :rule and_pos)
% 2.33/2.59  (step t3.t108 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.33/2.59  (step t3.t109 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.59  (step t3.t110 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule and_pos)
% 2.33/2.59  (step t3.t111 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.33/2.59  (step t3.t112 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule and_pos)
% 2.33/2.59  (step t3.t113 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))) :rule and_pos)
% 2.33/2.59  (step t3.t114 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule and_pos)
% 2.33/2.59  (step t3.t115 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule and_pos)
% 2.33/2.59  (step t3.t116 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) :rule and_pos)
% 2.33/2.59  (step t3.t117 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule and_pos)
% 2.33/2.59  (step t3.t118 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) :rule and_pos)
% 2.33/2.59  (step t3.t119 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule and_pos)
% 2.33/2.59  (step t3.t120 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.33/2.59  (step t3.t121 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) :rule and_pos)
% 2.33/2.59  (step t3.t122 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.33/2.59  (step t3.t123 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.33/2.59  (step t3.t124 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule and_pos)
% 2.33/2.59  (step t3.t125 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.33/2.59  (step t3.t126 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) :rule and_pos)
% 2.33/2.59  (step t3.t127 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) :rule and_pos)
% 2.33/2.59  (step t3.t128 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) :rule and_pos)
% 2.33/2.59  (step t3.t129 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) :rule and_pos)
% 2.33/2.59  (step t3.t130 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.33/2.59  (step t3.t131 (cl (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t3.t2 t3.t3 t3.t4 t3.t5 t3.t6 t3.t7 t3.t8 t3.t9 t3.t10 t3.t11 t3.t12 t3.t13 t3.t14 t3.t15 t3.t16 t3.t17 t3.t18 t3.t19 t3.t20 t3.t21 t3.t22 t3.t23 t3.t24 t3.t25 t3.t26 t3.t27 t3.t28 t3.t29 t3.t30 t3.t31 t3.t32 t3.t33 t3.t34 t3.t35 t3.t36 t3.t37 t3.t38 t3.t39 t3.t40 t3.t41 t3.t42 t3.t43 t3.t44 t3.t45 t3.t46 t3.t47 t3.t48 t3.t49 t3.t50 t3.t51 t3.t52 t3.t53 t3.t54 t3.t55 t3.t56 t3.t57 t3.t58 t3.t59 t3.t60 t3.t61 t3.t62 t3.t63 t3.t64 t3.t65 t3.t66 t3.t67 t3.t68 t3.t69 t3.t70 t3.t71 t3.t72 t3.t73 t3.t74 t3.t75 t3.t76 t3.t77 t3.t78 t3.t79 t3.t80 t3.t81 t3.t82 t3.t83 t3.t84 t3.t85 t3.t86 t3.t87 t3.t88 t3.t89 t3.t90 t3.t91 t3.t92 t3.t93 t3.t94 t3.t95 t3.t96 t3.t97 t3.t98 t3.t99 t3.t100 t3.t101 t3.t102 t3.t103 t3.t104 t3.t105 t3.t106 t3.t107 t3.t108 t3.t109 t3.t110 t3.t111 t3.t112 t3.t113 t3.t114 t3.t115 t3.t116 t3.t117 t3.t118 t3.t119 t3.t120 t3.t121 t3.t122 t3.t123 t3.t124 t3.t125 t3.t126 t3.t127 t3.t128 t3.t129 t3.t130))
% 2.41/2.61  (step t3.t132 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule reordering :premises (t3.t131))
% 2.41/2.63  (step t3.t133 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule contraction :premises (t3.t132))
% 2.41/2.63  (step t3.t134 (cl (=> (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule resolution :premises (t3.t1 t3.t133))
% 2.41/2.63  (step t3.t135 (cl (=> (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (not (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))) :rule implies_neg2)
% 2.41/2.63  (step t3.t136 (cl (=> (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (=> (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))) :rule resolution :premises (t3.t134 t3.t135))
% 2.41/2.63  (step t3.t137 (cl (=> (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))) :rule contraction :premises (t3.t136))
% 2.41/2.63  (step t3.t138 (cl (not (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule implies :premises (t3.t137))
% 2.41/2.63  (step t3.t139 (cl (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) (not (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) (not (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) (not (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) (not (= tptp.x (tptp.implies tptp.truth tptp.x))) (not (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) (not (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) (not (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= tptp.falsehood (tptp.not tptp.truth))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) (not (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) (not (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (not (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) (not (= tptp.truth (tptp.implies tptp.truth tptp.truth))) (not (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) (not (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) (not (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) (not (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (not (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) (not (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) (not (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) (not (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) (not (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) :rule and_neg)
% 2.41/2.63  (step t3.t140 (cl (and (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t3.t139 t3.a91 t3.a79 t3.a66 t3.a65 t3.a48 t3.a64 t3.a53 t3.a51 t3.a72 t3.a50 t3.a44 t3.a60 t3.a21 t3.a115 t3.a41 t3.a57 t3.a102 t3.a38 t3.a55 t3.a92 t3.a11 t3.a20 t3.a74 t3.a54 t3.a87 t3.a3 t3.a23 t3.a39 t3.a8 t3.a6 t3.a47 t3.a31 t3.a69 t3.a10 t3.a122 t3.a67 t3.a1 t3.a105 t3.a123 t3.a75 t3.a117 t3.a4 t3.a17 t3.a73 t3.a12 t3.a42 t3.a80 t3.a0 t3.a77 t3.a40 t3.a32 t3.a18 t3.a22 t3.a24 t3.a88 t3.a99 t3.a7 t3.a61 t3.a127 t3.a14 t3.a28 t3.a111 t3.a19 t3.a97 t3.a25 t3.a81 t3.a27 t3.a84 t3.a62 t3.a30 t3.a34 t3.a68 t3.a89 t3.a35 t3.a13 t3.a5 t3.a43 t3.a82 t3.a83 t3.a90 t3.a108 t3.a56 t3.a95 t3.a96 t3.a26 t3.a103 t3.a124 t3.a104 t3.a113 t3.a106 t3.a16 t3.a100 t3.a112 t3.a120 t3.a114 t3.a125 t3.a98 t3.a71 t3.a37 t3.a49 t3.a15 t3.a70 t3.a85 t3.a46 t3.a118 t3.a78 t3.a52 t3.a59 t3.a2 t3.a116 t3.a94 t3.a109 t3.a86 t3.a36 t3.a45 t3.a93 t3.a76 t3.a119 t3.a107 t3.a9 t3.a126 t3.a29 t3.a101 t3.a121 t3.a110 t3.a63 t3.a33 t3.a58))
% 2.41/2.63  (step t3.t141 (cl (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule resolution :premises (t3.t138 t3.t140))
% 2.41/2.63  (step t3 (cl (not (= tptp.falsehood (tptp.not tptp.truth))) (not (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (not (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))) (not (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) (not (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x)))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) (not (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (not (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= tptp.truth (tptp.implies tptp.truth tptp.truth))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (not (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (not (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) (not (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) (not (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) (not (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))) (not (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= tptp.x (tptp.implies tptp.truth tptp.x))) (not (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (not (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) (not (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) (not (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) (not (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) (not (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) (not (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) (not (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) (not (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule subproof :discharge (t3.a0 t3.a1 t3.a2 t3.a3 t3.a4 t3.a5 t3.a6 t3.a7 t3.a8 t3.a9 t3.a10 t3.a11 t3.a12 t3.a13 t3.a14 t3.a15 t3.a16 t3.a17 t3.a18 t3.a19 t3.a20 t3.a21 t3.a22 t3.a23 t3.a24 t3.a25 t3.a26 t3.a27 t3.a28 t3.a29 t3.a30 t3.a31 t3.a32 t3.a33 t3.a34 t3.a35 t3.a36 t3.a37 t3.a38 t3.a39 t3.a40 t3.a41 t3.a42 t3.a43 t3.a44 t3.a45 t3.a46 t3.a47 t3.a48 t3.a49 t3.a50 t3.a51 t3.a52 t3.a53 t3.a54 t3.a55 t3.a56 t3.a57 t3.a58 t3.a59 t3.a60 t3.a61 t3.a62 t3.a63 t3.a64 t3.a65 t3.a66 t3.a67 t3.a68 t3.a69 t3.a70 t3.a71 t3.a72 t3.a73 t3.a74 t3.a75 t3.a76 t3.a77 t3.a78 t3.a79 t3.a80 t3.a81 t3.a82 t3.a83 t3.a84 t3.a85 t3.a86 t3.a87 t3.a88 t3.a89 t3.a90 t3.a91 t3.a92 t3.a93 t3.a94 t3.a95 t3.a96 t3.a97 t3.a98 t3.a99 t3.a100 t3.a101 t3.a102 t3.a103 t3.a104 t3.a105 t3.a106 t3.a107 t3.a108 t3.a109 t3.a110 t3.a111 t3.a112 t3.a113 t3.a114 t3.a115 t3.a116 t3.a117 t3.a118 t3.a119 t3.a120 t3.a121 t3.a122 t3.a123 t3.a124 t3.a125 t3.a126 t3.a127))
% 2.41/2.63  (step t4 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.falsehood (tptp.not tptp.truth))) :rule and_pos)
% 2.41/2.63  (step t5 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.63  (step t6 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.41/2.63  (step t7 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule and_pos)
% 2.41/2.63  (step t8 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))) :rule and_pos)
% 2.41/2.63  (step t9 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x))) :rule and_pos)
% 2.41/2.63  (step t10 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.63  (step t11 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule and_pos)
% 2.41/2.63  (step t12 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x)))) :rule and_pos)
% 2.41/2.63  (step t13 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.41/2.63  (step t14 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule and_pos)
% 2.41/2.63  (step t15 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule and_pos)
% 2.41/2.63  (step t16 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.63  (step t17 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.truth (tptp.implies tptp.truth tptp.truth))) :rule and_pos)
% 2.41/2.63  (step t18 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) :rule and_pos)
% 2.41/2.63  (step t19 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) :rule and_pos)
% 2.41/2.63  (step t20 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.41/2.63  (step t21 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.41/2.63  (step t22 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) :rule and_pos)
% 2.41/2.63  (step t23 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) :rule and_pos)
% 2.41/2.63  (step t24 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) :rule and_pos)
% 2.41/2.63  (step t25 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule and_pos)
% 2.41/2.63  (step t26 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.41/2.63  (step t27 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule and_pos)
% 2.41/2.63  (step t28 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) :rule and_pos)
% 2.41/2.63  (step t29 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.41/2.63  (step t30 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule and_pos)
% 2.41/2.63  (step t31 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule and_pos)
% 2.41/2.63  (step t32 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.63  (step t33 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule and_pos)
% 2.41/2.63  (step t34 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.41/2.64  (step t35 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.41/2.64  (step t36 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.41/2.64  (step t37 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) :rule and_pos)
% 2.41/2.64  (step t38 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule and_pos)
% 2.41/2.64  (step t39 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) :rule and_pos)
% 2.41/2.64  (step t40 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) :rule and_pos)
% 2.41/2.64  (step t41 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.64  (step t42 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule and_pos)
% 2.41/2.64  (step t43 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.41/2.64  (step t44 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule and_pos)
% 2.41/2.64  (step t45 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.64  (step t46 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) :rule and_pos)
% 2.41/2.64  (step t47 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) :rule and_pos)
% 2.41/2.64  (step t48 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.41/2.64  (step t49 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule and_pos)
% 2.41/2.64  (step t50 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) :rule and_pos)
% 2.41/2.64  (step t51 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.41/2.64  (step t52 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) :rule and_pos)
% 2.41/2.64  (step t53 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule and_pos)
% 2.41/2.64  (step t54 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))) :rule and_pos)
% 2.41/2.64  (step t55 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))) :rule and_pos)
% 2.41/2.64  (step t56 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.64  (step t57 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) :rule and_pos)
% 2.41/2.64  (step t58 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule and_pos)
% 2.41/2.64  (step t59 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.41/2.64  (step t60 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule and_pos)
% 2.41/2.64  (step t61 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule and_pos)
% 2.41/2.64  (step t62 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.64  (step t63 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule and_pos)
% 2.41/2.64  (step t64 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) :rule and_pos)
% 2.41/2.64  (step t65 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) :rule and_pos)
% 2.41/2.64  (step t66 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.41/2.64  (step t67 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) :rule and_pos)
% 2.41/2.64  (step t68 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.64  (step t69 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.41/2.64  (step t70 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.41/2.64  (step t71 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.41/2.64  (step t72 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.64  (step t73 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.x (tptp.implies tptp.truth tptp.x))) :rule and_pos)
% 2.41/2.64  (step t74 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) :rule and_pos)
% 2.41/2.64  (step t75 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.41/2.64  (step t76 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.64  (step t77 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.41/2.64  (step t78 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.64  (step t79 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.41/2.64  (step t80 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule and_pos)
% 2.41/2.64  (step t81 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) :rule and_pos)
% 2.41/2.64  (step t82 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.41/2.64  (step t83 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))) :rule and_pos)
% 2.41/2.64  (step t84 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.41/2.64  (step t85 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) :rule and_pos)
% 2.41/2.64  (step t86 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) :rule and_pos)
% 2.41/2.64  (step t87 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.41/2.64  (step t88 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule and_pos)
% 2.41/2.64  (step t89 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.41/2.64  (step t90 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule and_pos)
% 2.41/2.64  (step t91 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule and_pos)
% 2.41/2.64  (step t92 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) :rule and_pos)
% 2.41/2.64  (step t93 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule and_pos)
% 2.41/2.64  (step t94 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.41/2.64  (step t95 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule and_pos)
% 2.41/2.64  (step t96 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) :rule and_pos)
% 2.41/2.64  (step t97 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) :rule and_pos)
% 2.41/2.64  (step t98 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))) :rule and_pos)
% 2.41/2.64  (step t99 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.41/2.64  (step t100 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule and_pos)
% 2.41/2.64  (step t101 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.41/2.64  (step t102 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule and_pos)
% 2.41/2.64  (step t103 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.41/2.64  (step t104 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) :rule and_pos)
% 2.41/2.64  (step t105 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.41/2.64  (step t106 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule and_pos)
% 2.41/2.64  (step t107 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule and_pos)
% 2.41/2.65  (step t108 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) :rule and_pos)
% 2.41/2.65  (step t109 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.41/2.65  (step t110 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) :rule and_pos)
% 2.41/2.65  (step t111 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) :rule and_pos)
% 2.41/2.65  (step t112 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule and_pos)
% 2.41/2.65  (step t113 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule and_pos)
% 2.41/2.65  (step t114 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) :rule and_pos)
% 2.41/2.65  (step t115 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.41/2.65  (step t116 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule and_pos)
% 2.41/2.65  (step t117 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.41/2.65  (step t118 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) :rule and_pos)
% 2.41/2.65  (step t119 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) :rule and_pos)
% 2.41/2.65  (step t120 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule and_pos)
% 2.41/2.65  (step t121 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.41/2.65  (step t122 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) :rule and_pos)
% 2.41/2.65  (step t123 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule and_pos)
% 2.41/2.65  (step t124 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule and_pos)
% 2.41/2.65  (step t125 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) :rule and_pos)
% 2.41/2.65  (step t126 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) :rule and_pos)
% 2.41/2.65  (step t127 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.41/2.65  (step t128 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule and_pos)
% 2.41/2.65  (step t129 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule and_pos)
% 2.41/2.65  (step t130 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule and_pos)
% 2.41/2.65  (step t131 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule and_pos)
% 2.41/2.65  (step t132 (cl (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))))) :rule resolution :premises (t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 t21 t22 t23 t24 t25 t26 t27 t28 t29 t30 t31 t32 t33 t34 t35 t36 t37 t38 t39 t40 t41 t42 t43 t44 t45 t46 t47 t48 t49 t50 t51 t52 t53 t54 t55 t56 t57 t58 t59 t60 t61 t62 t63 t64 t65 t66 t67 t68 t69 t70 t71 t72 t73 t74 t75 t76 t77 t78 t79 t80 t81 t82 t83 t84 t85 t86 t87 t88 t89 t90 t91 t92 t93 t94 t95 t96 t97 t98 t99 t100 t101 t102 t103 t104 t105 t106 t107 t108 t109 t110 t111 t112 t113 t114 t115 t116 t117 t118 t119 t120 t121 t122 t123 t124 t125 t126 t127 t128 t129 t130 t131))
% 2.41/2.67  (step t133 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule reordering :premises (t132))
% 2.41/2.68  (step t134 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule contraction :premises (t133))
% 2.41/2.68  (step t135 (cl (=> (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule resolution :premises (t2 t134))
% 2.41/2.68  (step t136 (cl (=> (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (not (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))) :rule implies_neg2)
% 2.41/2.68  (step t137 (cl (=> (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (=> (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))) :rule resolution :premises (t135 t136))
% 2.41/2.68  (step t138 (cl (=> (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))) :rule contraction :premises (t137))
% 2.41/2.68  (step t139 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= tptp.x (tptp.implies tptp.truth tptp.x)) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule implies :premises (t138))
% 2.41/2.68  (step t140 (cl (not (= tptp.falsehood (tptp.not tptp.truth))) (not (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (not (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))) (not (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) (not (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x)))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) (not (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (not (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= tptp.truth (tptp.implies tptp.truth tptp.truth))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (not (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (not (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) (not (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) (not (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) (not (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))) (not (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= tptp.x (tptp.implies tptp.truth tptp.x))) (not (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (not (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) (not (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) (not (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) (not (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) (not (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) (not (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) (not (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) (not (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule resolution :premises (t1 t139))
% 2.41/2.68  (step t141 (cl (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (not (= tptp.falsehood (tptp.not tptp.truth))) (not (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (not (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))) (not (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) (not (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x)))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) (not (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (not (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= tptp.truth (tptp.implies tptp.truth tptp.truth))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (not (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (not (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) (not (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) (not (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) (not (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))) (not (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= tptp.x (tptp.implies tptp.truth tptp.x))) (not (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (not (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))) (not (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) (not (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) (not (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) (not (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) (not (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) (not (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) (not (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) (not (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) :rule reordering :premises (t140))
% 2.41/2.68  (step t142 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t143)
% 2.41/2.68  (assume t143.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))))
% 2.41/2.68  (step t143.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (:= Z (tptp.and (tptp.not tptp.x) tptp.truth))))
% 2.41/2.68  (step t143.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule or :premises (t143.t1))
% 2.41/2.68  (step t143.t3 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule resolution :premises (t143.t2 t143.a0))
% 2.41/2.68  (step t143 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule subproof :discharge (t143.a0))
% 2.41/2.68  (step t144 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule resolution :premises (t142 t143))
% 2.41/2.68  (step t145 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) :rule implies_neg2)
% 2.41/2.68  (step t146 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) :rule resolution :premises (t144 t145))
% 2.41/2.68  (step t147 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth))))))) :rule contraction :premises (t146))
% 2.41/2.68  (step t148 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule implies :premises (t147))
% 2.41/2.68  (step t149 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))) tptp.truth)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))))) (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) :rule equiv_pos2)
% 2.41/2.68  (anchor :step t150 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (Z $$unsorted) (:= Z Z)))
% 2.41/2.68  (step t150.t1 (cl (= X X)) :rule refl)
% 2.41/2.68  (step t150.t2 (cl (= Y Y)) :rule refl)
% 2.41/2.68  (step t150.t3 (cl (= Z Z)) :rule refl)
% 2.41/2.68  (step t150.t4 (cl (= (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))) tptp.truth) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) :rule all_simplify)
% 2.41/2.68  (step t150 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))) tptp.truth)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))))) :rule bind)
% 2.41/2.68  (step t151 (cl (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) :rule resolution :premises (t149 t150 a1))
% 2.41/2.68  (step t152 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule resolution :premises (t148 t151))
% 2.41/2.68  (step t153 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t154)
% 2.41/2.68  (assume t154.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 2.41/2.68  (step t154.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.41/2.68  (step t154.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule or :premises (t154.t1))
% 2.41/2.68  (step t154.t3 (cl (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t154.t2 t154.a0))
% 2.41/2.68  (step t154 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule subproof :discharge (t154.a0))
% 2.41/2.68  (step t155 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t153 t154))
% 2.41/2.68  (step t156 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule implies_neg2)
% 2.41/2.68  (step t157 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t155 t156))
% 2.41/2.68  (step t158 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule contraction :premises (t157))
% 2.41/2.68  (step t159 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies :premises (t158))
% 2.41/2.68  (step t160 (cl (not (= (forall ((X $$unsorted)) (= (tptp.implies tptp.truth X) X)) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))) (not (forall ((X $$unsorted)) (= (tptp.implies tptp.truth X) X))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule equiv_pos2)
% 2.41/2.68  (anchor :step t161 :args ((X $$unsorted) (:= X X)))
% 2.41/2.68  (step t161.t1 (cl (= X X)) :rule refl)
% 2.41/2.68  (step t161.t2 (cl (= (= (tptp.implies tptp.truth X) X) (= X (tptp.implies tptp.truth X)))) :rule all_simplify)
% 2.41/2.68  (step t161 (cl (= (forall ((X $$unsorted)) (= (tptp.implies tptp.truth X) X)) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))) :rule bind)
% 2.41/2.68  (step t162 (cl (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule resolution :premises (t160 t161 a0))
% 2.41/2.68  (step t163 (cl (= (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t159 t162))
% 2.41/2.68  (step t164 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule equiv_pos2)
% 2.41/2.68  (step t165 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))) :rule refl)
% 2.41/2.68  (step t166 (cl (= (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule all_simplify)
% 2.41/2.68  (step t167 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule cong :premises (t165 t166))
% 2.41/2.68  (step t168 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t169)
% 2.41/2.68  (assume t169.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.68  (step t169.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (:= Y (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))
% 2.41/2.68  (step t169.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule or :premises (t169.t1))
% 2.41/2.68  (step t169.t3 (cl (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule resolution :premises (t169.t2 t169.a0))
% 2.41/2.68  (step t169 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule subproof :discharge (t169.a0))
% 2.41/2.68  (step t170 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule resolution :premises (t168 t169))
% 2.41/2.68  (step t171 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (not (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule implies_neg2)
% 2.41/2.68  (step t172 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule resolution :premises (t170 t171))
% 2.41/2.68  (step t173 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule contraction :premises (t172))
% 2.41/2.68  (step t174 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule resolution :premises (t164 t167 t173))
% 2.41/2.68  (step t175 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule implies :premises (t174))
% 2.41/2.68  (step t176 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule resolution :premises (t175 a12))
% 2.41/2.68  (step t177 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule equiv_pos2)
% 2.41/2.68  (step t178 (cl (= (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule all_simplify)
% 2.41/2.68  (step t179 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule cong :premises (t165 t178))
% 2.41/2.68  (step t180 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t181)
% 2.41/2.68  (assume t181.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.68  (step t181.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (:= Y (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.41/2.68  (step t181.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule or :premises (t181.t1))
% 2.41/2.68  (step t181.t3 (cl (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule resolution :premises (t181.t2 t181.a0))
% 2.41/2.68  (step t181 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule subproof :discharge (t181.a0))
% 2.41/2.68  (step t182 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule resolution :premises (t180 t181))
% 2.41/2.68  (step t183 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule implies_neg2)
% 2.41/2.68  (step t184 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule resolution :premises (t182 t183))
% 2.41/2.68  (step t185 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule contraction :premises (t184))
% 2.41/2.68  (step t186 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t177 t179 t185))
% 2.41/2.68  (step t187 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule implies :premises (t186))
% 2.41/2.68  (step t188 (cl (= (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and_star (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t187 a12))
% 2.41/2.68  (step t189 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t190)
% 2.41/2.68  (assume t190.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.68  (step t190.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (:= Y (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))
% 2.41/2.68  (step t190.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule or :premises (t190.t1))
% 2.41/2.68  (step t190.t3 (cl (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t190.t2 t190.a0))
% 2.41/2.68  (step t190 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule subproof :discharge (t190.a0))
% 2.41/2.68  (step t191 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t189 t190))
% 2.41/2.68  (step t192 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule implies_neg2)
% 2.41/2.68  (step t193 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t191 t192))
% 2.41/2.68  (step t194 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule contraction :premises (t193))
% 2.41/2.68  (step t195 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies :premises (t194))
% 2.41/2.68  (step t196 (cl (= (tptp.and (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t195 a9))
% 2.41/2.68  (step t197 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t198)
% 2.41/2.68  (assume t198.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.68  (step t198.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))
% 2.41/2.68  (step t198.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) :rule or :premises (t198.t1))
% 2.41/2.68  (step t198.t3 (cl (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) :rule resolution :premises (t198.t2 t198.a0))
% 2.41/2.68  (step t198 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) :rule subproof :discharge (t198.a0))
% 2.41/2.68  (step t199 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) :rule resolution :premises (t197 t198))
% 2.41/2.68  (step t200 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) (not (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)))) :rule implies_neg2)
% 2.41/2.68  (step t201 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)))) :rule resolution :premises (t199 t200))
% 2.41/2.68  (step t202 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood)))) :rule contraction :premises (t201))
% 2.41/2.68  (step t203 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) :rule implies :premises (t202))
% 2.41/2.68  (step t204 (cl (= (tptp.and tptp.falsehood (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) tptp.falsehood))) :rule resolution :premises (t203 a9))
% 2.41/2.68  (step t205 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t206)
% 2.41/2.68  (assume t206.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.68  (step t206.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))))) :rule forall_inst :args ((:= X (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) (:= Y (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) (:= Z tptp.falsehood)))
% 2.41/2.68  (step t206.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) :rule or :premises (t206.t1))
% 2.41/2.68  (step t206.t3 (cl (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) :rule resolution :premises (t206.t2 t206.a0))
% 2.41/2.68  (step t206 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) :rule subproof :discharge (t206.a0))
% 2.41/2.68  (step t207 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) :rule resolution :premises (t205 t206))
% 2.41/2.68  (step t208 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) (not (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))))) :rule implies_neg2)
% 2.41/2.68  (step t209 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))))) :rule resolution :premises (t207 t208))
% 2.41/2.68  (step t210 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood))))) :rule contraction :premises (t209))
% 2.41/2.68  (step t211 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) :rule implies :premises (t210))
% 2.41/2.68  (step t212 (cl (= (tptp.and (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x)) tptp.falsehood) (tptp.and (tptp.not (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood)))) :rule resolution :premises (t211 a8))
% 2.41/2.68  (step t213 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t214)
% 2.41/2.68  (assume t214.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.68  (step t214.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (:= Y tptp.truth) (:= Z (tptp.not tptp.truth))))
% 2.41/2.68  (step t214.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule or :premises (t214.t1))
% 2.41/2.68  (step t214.t3 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule resolution :premises (t214.t2 t214.a0))
% 2.41/2.68  (step t214 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule subproof :discharge (t214.a0))
% 2.41/2.68  (step t215 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule resolution :premises (t213 t214))
% 2.41/2.68  (step t216 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule implies_neg2)
% 2.41/2.68  (step t217 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule resolution :premises (t215 t216))
% 2.41/2.68  (step t218 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule contraction :premises (t217))
% 2.41/2.68  (step t219 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule implies :premises (t218))
% 2.41/2.68  (step t220 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.truth) (tptp.not tptp.truth)) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule resolution :premises (t219 a8))
% 2.41/2.68  (step t221 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t222)
% 2.41/2.68  (assume t222.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.68  (step t222.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y tptp.truth) (:= Z (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.41/2.68  (step t222.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule or :premises (t222.t1))
% 2.41/2.68  (step t222.t3 (cl (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t222.t2 t222.a0))
% 2.41/2.68  (step t222 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule subproof :discharge (t222.a0))
% 2.41/2.68  (step t223 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t221 t222))
% 2.41/2.68  (step t224 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies_neg2)
% 2.41/2.68  (step t225 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t223 t224))
% 2.41/2.68  (step t226 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule contraction :premises (t225))
% 2.41/2.68  (step t227 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule implies :premises (t226))
% 2.41/2.68  (step t228 (cl (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t227 a8))
% 2.41/2.68  (step t229 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t230)
% 2.41/2.68  (assume t230.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.68  (step t230.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y tptp.truth) (:= Z tptp.x)))
% 2.41/2.68  (step t230.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) :rule or :premises (t230.t1))
% 2.41/2.68  (step t230.t3 (cl (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) :rule resolution :premises (t230.t2 t230.a0))
% 2.41/2.68  (step t230 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) :rule subproof :discharge (t230.a0))
% 2.41/2.68  (step t231 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) :rule resolution :premises (t229 t230))
% 2.41/2.68  (step t232 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) (not (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))))) :rule implies_neg2)
% 2.41/2.68  (step t233 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))))) :rule resolution :premises (t231 t232))
% 2.41/2.68  (step t234 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x))))) :rule contraction :premises (t233))
% 2.41/2.68  (step t235 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) :rule implies :premises (t234))
% 2.41/2.68  (step t236 (cl (= (tptp.and (tptp.and (tptp.not tptp.falsehood) tptp.truth) tptp.x) (tptp.and (tptp.not tptp.falsehood) (tptp.and tptp.truth tptp.x)))) :rule resolution :premises (t235 a8))
% 2.41/2.68  (step t237 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t238)
% 2.41/2.68  (assume t238.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.68  (step t238.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.not tptp.truth)) (:= Z (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))
% 2.41/2.68  (step t238.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule or :premises (t238.t1))
% 2.41/2.68  (step t238.t3 (cl (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t238.t2 t238.a0))
% 2.41/2.68  (step t238 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule subproof :discharge (t238.a0))
% 2.41/2.68  (step t239 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t237 t238))
% 2.41/2.68  (step t240 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule implies_neg2)
% 2.41/2.68  (step t241 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t239 t240))
% 2.41/2.68  (step t242 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule contraction :premises (t241))
% 2.41/2.68  (step t243 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies :premises (t242))
% 2.41/2.68  (step t244 (cl (= (tptp.and (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.and (tptp.not tptp.truth) (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t243 a8))
% 2.41/2.68  (step t245 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t246)
% 2.41/2.68  (assume t246.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.68  (step t246.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))))) :rule forall_inst :args ((:= X (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x)) (:= Y (tptp.not tptp.x)) (:= Z tptp.x)))
% 2.41/2.68  (step t246.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule or :premises (t246.t1))
% 2.41/2.68  (step t246.t3 (cl (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule resolution :premises (t246.t2 t246.a0))
% 2.41/2.68  (step t246 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule subproof :discharge (t246.a0))
% 2.41/2.68  (step t247 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule resolution :premises (t245 t246))
% 2.41/2.68  (step t248 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) (not (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))))) :rule implies_neg2)
% 2.41/2.68  (step t249 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))))) :rule resolution :premises (t247 t248))
% 2.41/2.68  (step t250 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x))))) :rule contraction :premises (t249))
% 2.41/2.68  (step t251 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule implies :premises (t250))
% 2.41/2.68  (step t252 (cl (= (tptp.and (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) tptp.x) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule resolution :premises (t251 a8))
% 2.41/2.68  (step t253 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t254)
% 2.41/2.68  (assume t254.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.68  (step t254.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (:= Y (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))
% 2.41/2.68  (step t254.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) :rule or :premises (t254.t1))
% 2.41/2.68  (step t254.t3 (cl (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) :rule resolution :premises (t254.t2 t254.a0))
% 2.41/2.68  (step t254 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) :rule subproof :discharge (t254.a0))
% 2.41/2.68  (step t255 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) :rule resolution :premises (t253 t254))
% 2.41/2.68  (step t256 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))))) :rule implies_neg2)
% 2.41/2.68  (step t257 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))))) :rule resolution :premises (t255 t256))
% 2.41/2.68  (step t258 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))))) :rule contraction :premises (t257))
% 2.41/2.68  (step t259 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) :rule implies :premises (t258))
% 2.41/2.68  (step t260 (cl (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))))) :rule resolution :premises (t259 a7))
% 2.41/2.68  (step t261 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t262)
% 2.41/2.68  (assume t262.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.68  (step t262.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (:= Y (tptp.not (tptp.not (tptp.not tptp.falsehood))))))
% 2.41/2.68  (step t262.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) :rule or :premises (t262.t1))
% 2.41/2.68  (step t262.t3 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t262.t2 t262.a0))
% 2.41/2.68  (step t262 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) :rule subproof :discharge (t262.a0))
% 2.41/2.68  (step t263 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t261 t262))
% 2.41/2.68  (step t264 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))))) :rule implies_neg2)
% 2.41/2.68  (step t265 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))))) :rule resolution :premises (t263 t264))
% 2.41/2.68  (step t266 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood))))))))) :rule contraction :premises (t265))
% 2.41/2.68  (step t267 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) :rule implies :premises (t266))
% 2.41/2.68  (step t268 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t267 a7))
% 2.41/2.68  (step t269 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t270)
% 2.41/2.68  (assume t270.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.68  (step t270.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (:= Y (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.41/2.68  (step t270.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule or :premises (t270.t1))
% 2.41/2.68  (step t270.t3 (cl (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t270.t2 t270.a0))
% 2.41/2.68  (step t270 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule subproof :discharge (t270.a0))
% 2.41/2.68  (step t271 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t269 t270))
% 2.41/2.68  (step t272 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule implies_neg2)
% 2.41/2.68  (step t273 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t271 t272))
% 2.41/2.68  (step t274 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule contraction :premises (t273))
% 2.41/2.68  (step t275 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies :premises (t274))
% 2.41/2.68  (step t276 (cl (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t275 a7))
% 2.41/2.68  (step t277 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t278)
% 2.41/2.68  (assume t278.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.68  (step t278.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule forall_inst :args ((:= X (tptp.not tptp.truth)) (:= Y (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.41/2.68  (step t278.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule or :premises (t278.t1))
% 2.41/2.68  (step t278.t3 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule resolution :premises (t278.t2 t278.a0))
% 2.41/2.68  (step t278 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule subproof :discharge (t278.a0))
% 2.41/2.68  (step t279 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule resolution :premises (t277 t278))
% 2.41/2.68  (step t280 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule implies_neg2)
% 2.41/2.68  (step t281 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule resolution :premises (t279 t280))
% 2.41/2.68  (step t282 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule contraction :premises (t281))
% 2.41/2.68  (step t283 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule implies :premises (t282))
% 2.41/2.68  (step t284 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))) :rule resolution :premises (t283 a6))
% 2.41/2.68  (step t285 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t286)
% 2.41/2.68  (assume t286.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.68  (step t286.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule forall_inst :args ((:= X (tptp.and tptp.x (tptp.not tptp.truth))) (:= Y (tptp.not (tptp.not tptp.falsehood)))))
% 2.41/2.68  (step t286.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule or :premises (t286.t1))
% 2.41/2.68  (step t286.t3 (cl (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t286.t2 t286.a0))
% 2.41/2.68  (step t286 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule subproof :discharge (t286.a0))
% 2.41/2.68  (step t287 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t285 t286))
% 2.41/2.68  (step t288 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule implies_neg2)
% 2.41/2.68  (step t289 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t287 t288))
% 2.41/2.68  (step t290 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule contraction :premises (t289))
% 2.41/2.68  (step t291 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule implies :premises (t290))
% 2.41/2.68  (step t292 (cl (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t291 a6))
% 2.41/2.68  (step t293 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t294)
% 2.41/2.68  (assume t294.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.68  (step t294.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)))) :rule forall_inst :args ((:= X tptp.x) (:= Y tptp.falsehood)))
% 2.41/2.68  (step t294.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) :rule or :premises (t294.t1))
% 2.41/2.68  (step t294.t3 (cl (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) :rule resolution :premises (t294.t2 t294.a0))
% 2.41/2.68  (step t294 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) :rule subproof :discharge (t294.a0))
% 2.41/2.68  (step t295 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) :rule resolution :premises (t293 t294))
% 2.41/2.68  (step t296 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) (not (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)))) :rule implies_neg2)
% 2.41/2.68  (step t297 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)))) :rule resolution :premises (t295 t296))
% 2.41/2.68  (step t298 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x)))) :rule contraction :premises (t297))
% 2.41/2.68  (step t299 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) :rule implies :premises (t298))
% 2.41/2.68  (step t300 (cl (= (tptp.or tptp.x tptp.falsehood) (tptp.or tptp.falsehood tptp.x))) :rule resolution :premises (t299 a6))
% 2.41/2.68  (step t301 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z)))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t302)
% 2.41/2.68  (assume t302.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z)))))
% 2.41/2.68  (step t302.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (:= Y (tptp.and tptp.truth (tptp.not tptp.truth))) (:= Z (tptp.and (tptp.not tptp.truth) tptp.truth))))
% 2.41/2.68  (step t302.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule or :premises (t302.t1))
% 2.41/2.68  (step t302.t3 (cl (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule resolution :premises (t302.t2 t302.a0))
% 2.41/2.68  (step t302 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule subproof :discharge (t302.a0))
% 2.41/2.68  (step t303 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z)))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule resolution :premises (t301 t302))
% 2.41/2.68  (step t304 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z)))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))))) :rule implies_neg2)
% 2.41/2.68  (step t305 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z)))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z)))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))))) :rule resolution :premises (t303 t304))
% 2.41/2.68  (step t306 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z)))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))))) :rule contraction :premises (t305))
% 2.41/2.68  (step t307 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.or (tptp.or X Y) Z) (tptp.or X (tptp.or Y Z))))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule implies :premises (t306))
% 2.41/2.68  (step t308 (cl (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and tptp.truth (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule resolution :premises (t307 a5))
% 2.41/2.68  (step t309 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t310)
% 2.41/2.68  (assume t310.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.68  (step t310.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (:= Y (tptp.not tptp.truth))))
% 2.41/2.68  (step t310.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule or :premises (t310.t1))
% 2.41/2.68  (step t310.t3 (cl (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule resolution :premises (t310.t2 t310.a0))
% 2.41/2.68  (step t310 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule subproof :discharge (t310.a0))
% 2.41/2.68  (step t311 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule resolution :premises (t309 t310))
% 2.41/2.68  (step t312 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))))) :rule implies_neg2)
% 2.41/2.68  (step t313 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))))) :rule resolution :premises (t311 t312))
% 2.41/2.68  (step t314 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth))))) :rule contraction :premises (t313))
% 2.41/2.68  (step t315 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule implies :premises (t314))
% 2.41/2.68  (step t316 (cl (= (tptp.or (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule resolution :premises (t315 a4))
% 2.41/2.68  (step t317 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t318)
% 2.41/2.68  (assume t318.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.68  (step t318.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y tptp.x)))
% 2.41/2.68  (step t318.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) :rule or :premises (t318.t1))
% 2.41/2.68  (step t318.t3 (cl (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) :rule resolution :premises (t318.t2 t318.a0))
% 2.41/2.68  (step t318 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) :rule subproof :discharge (t318.a0))
% 2.41/2.68  (step t319 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) :rule resolution :premises (t317 t318))
% 2.41/2.68  (step t320 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) (not (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)))) :rule implies_neg2)
% 2.41/2.68  (step t321 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)))) :rule resolution :premises (t319 t320))
% 2.41/2.68  (step t322 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x)))) :rule contraction :premises (t321))
% 2.41/2.68  (step t323 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) :rule implies :premises (t322))
% 2.41/2.68  (step t324 (cl (= (tptp.or tptp.falsehood tptp.x) (tptp.implies (tptp.not tptp.falsehood) tptp.x))) :rule resolution :premises (t323 a4))
% 2.41/2.68  (step t325 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t326)
% 2.41/2.68  (assume t326.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.68  (step t326.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (:= Y (tptp.not tptp.truth))))
% 2.41/2.68  (step t326.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) :rule or :premises (t326.t1))
% 2.41/2.68  (step t326.t3 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) :rule resolution :premises (t326.t2 t326.a0))
% 2.41/2.68  (step t326 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) :rule subproof :discharge (t326.a0))
% 2.41/2.68  (step t327 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) :rule resolution :premises (t325 t326))
% 2.41/2.68  (step t328 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))))) :rule implies_neg2)
% 2.41/2.68  (step t329 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))))) :rule resolution :premises (t327 t328))
% 2.41/2.68  (step t330 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth))))) :rule contraction :premises (t329))
% 2.41/2.68  (step t331 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) :rule implies :premises (t330))
% 2.41/2.68  (step t332 (cl (= (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.not tptp.truth)))) :rule resolution :premises (t331 a4))
% 2.41/2.68  (step t333 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t334)
% 2.41/2.68  (assume t334.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.68  (step t334.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule forall_inst :args ((:= X (tptp.not tptp.truth)) (:= Y (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.41/2.68  (step t334.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule or :premises (t334.t1))
% 2.41/2.68  (step t334.t3 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t334.t2 t334.a0))
% 2.41/2.68  (step t334 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule subproof :discharge (t334.a0))
% 2.41/2.68  (step t335 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t333 t334))
% 2.41/2.68  (step t336 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule implies_neg2)
% 2.41/2.68  (step t337 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t335 t336))
% 2.41/2.68  (step t338 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule contraction :premises (t337))
% 2.41/2.68  (step t339 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies :premises (t338))
% 2.41/2.68  (step t340 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t339 a4))
% 2.41/2.68  (step t341 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t342)
% 2.41/2.68  (assume t342.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))))
% 2.41/2.68  (step t342.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.41/2.68  (step t342.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) :rule or :premises (t342.t1))
% 2.41/2.68  (step t342.t3 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) :rule resolution :premises (t342.t2 t342.a0))
% 2.41/2.68  (step t342 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) :rule subproof :discharge (t342.a0))
% 2.41/2.68  (step t343 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) :rule resolution :premises (t341 t342))
% 2.41/2.68  (step t344 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))))) :rule implies_neg2)
% 2.41/2.68  (step t345 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))))) :rule resolution :premises (t343 t344))
% 2.41/2.68  (step t346 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood))))) :rule contraction :premises (t345))
% 2.41/2.68  (step t347 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) :rule implies :premises (t346))
% 2.41/2.68  (step t348 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)) tptp.truth)) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) :rule equiv_pos2)
% 2.41/2.68  (anchor :step t349 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 2.41/2.68  (step t349.t1 (cl (= X X)) :rule refl)
% 2.41/2.68  (step t349.t2 (cl (= Y Y)) :rule refl)
% 2.41/2.68  (step t349.t3 (cl (= (= (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)) tptp.truth) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) :rule all_simplify)
% 2.41/2.68  (step t349 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)) tptp.truth)) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))))) :rule bind)
% 2.41/2.68  (step t350 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) :rule resolution :premises (t348 t349 a3))
% 2.41/2.68  (step t351 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.implies (tptp.and tptp.x (tptp.not tptp.truth)) tptp.falsehood)))) :rule resolution :premises (t347 t350))
% 2.41/2.68  (step t352 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t353)
% 2.41/2.68  (assume t353.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 2.41/2.68  (step t353.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (:= Y (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.41/2.68  (step t353.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule or :premises (t353.t1))
% 2.41/2.68  (step t353.t3 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t353.t2 t353.a0))
% 2.41/2.68  (step t353 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule subproof :discharge (t353.a0))
% 2.41/2.68  (step t354 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t352 t353))
% 2.41/2.68  (step t355 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule implies_neg2)
% 2.41/2.68  (step t356 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule resolution :premises (t354 t355))
% 2.41/2.68  (step t357 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule contraction :premises (t356))
% 2.41/2.68  (step t358 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule implies :premises (t357))
% 2.41/2.68  (step t359 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t358 a2))
% 2.41/2.68  (step t360 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 2.41/2.68  (anchor :step t361)
% 2.41/2.68  (assume t361.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 2.41/2.68  (step t361.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not (tptp.not tptp.x)))) (:= Y (tptp.not (tptp.not tptp.falsehood)))))
% 2.41/2.68  (step t361.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule or :premises (t361.t1))
% 2.41/2.69  (step t361.t3 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t361.t2 t361.a0))
% 2.41/2.69  (step t361 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule subproof :discharge (t361.a0))
% 2.41/2.69  (step t362 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t360 t361))
% 2.41/2.69  (step t363 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule implies_neg2)
% 2.41/2.69  (step t364 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t362 t363))
% 2.41/2.69  (step t365 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule contraction :premises (t364))
% 2.41/2.69  (step t366 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule implies :premises (t365))
% 2.41/2.69  (step t367 (cl (= (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t366 a2))
% 2.41/2.69  (step t368 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t369)
% 2.41/2.69  (assume t369.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 2.41/2.69  (step t369.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.41/2.69  (step t369.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule or :premises (t369.t1))
% 2.41/2.69  (step t369.t3 (cl (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t369.t2 t369.a0))
% 2.41/2.69  (step t369 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule subproof :discharge (t369.a0))
% 2.41/2.69  (step t370 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t368 t369))
% 2.41/2.69  (step t371 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule implies_neg2)
% 2.41/2.69  (step t372 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t370 t371))
% 2.41/2.69  (step t373 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule contraction :premises (t372))
% 2.41/2.69  (step t374 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule implies :premises (t373))
% 2.41/2.69  (step t375 (cl (= (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.implies tptp.truth (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t374 t162))
% 2.41/2.69  (step t376 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t377)
% 2.41/2.69  (assume t377.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 2.41/2.69  (step t377.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))))) :rule forall_inst :args ((:= X (tptp.not tptp.x))))
% 2.41/2.69  (step t377.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) :rule or :premises (t377.t1))
% 2.41/2.69  (step t377.t3 (cl (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) :rule resolution :premises (t377.t2 t377.a0))
% 2.41/2.69  (step t377 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) :rule subproof :discharge (t377.a0))
% 2.41/2.69  (step t378 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) :rule resolution :premises (t376 t377))
% 2.41/2.69  (step t379 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) (not (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))))) :rule implies_neg2)
% 2.41/2.69  (step t380 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))))) :rule resolution :premises (t378 t379))
% 2.41/2.69  (step t381 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x))))) :rule contraction :premises (t380))
% 2.41/2.69  (step t382 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) :rule implies :premises (t381))
% 2.41/2.69  (step t383 (cl (= (tptp.not tptp.x) (tptp.implies tptp.truth (tptp.not tptp.x)))) :rule resolution :premises (t382 t162))
% 2.41/2.69  (step t384 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t385)
% 2.41/2.69  (assume t385.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 2.41/2.69  (step t385.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule forall_inst :args ((:= X (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.41/2.69  (step t385.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) :rule or :premises (t385.t1))
% 2.41/2.69  (step t385.t3 (cl (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t385.t2 t385.a0))
% 2.41/2.69  (step t385 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) :rule subproof :discharge (t385.a0))
% 2.41/2.69  (step t386 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t384 t385))
% 2.41/2.69  (step t387 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule implies_neg2)
% 2.41/2.69  (step t388 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t386 t387))
% 2.41/2.69  (step t389 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule contraction :premises (t388))
% 2.41/2.69  (step t390 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) :rule implies :premises (t389))
% 2.41/2.69  (step t391 (cl (= (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t390 t162))
% 2.41/2.69  (step t392 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t393)
% 2.41/2.69  (assume t393.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t393.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (:= Y tptp.falsehood)))
% 2.41/2.69  (step t393.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule or :premises (t393.t1))
% 2.41/2.69  (step t393.t3 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t393.t2 t393.a0))
% 2.41/2.69  (step t393 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule subproof :discharge (t393.a0))
% 2.41/2.69  (step t394 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t392 t393))
% 2.41/2.69  (step t395 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (not (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule implies_neg2)
% 2.41/2.69  (step t396 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule resolution :premises (t394 t395))
% 2.41/2.69  (step t397 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule contraction :premises (t396))
% 2.41/2.69  (step t398 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule implies :premises (t397))
% 2.41/2.69  (step t399 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) tptp.falsehood) (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t398 a9))
% 2.41/2.69  (step t400 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule equiv_pos2)
% 2.41/2.69  (step t401 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))) :rule refl)
% 2.41/2.69  (step t402 (cl (= (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule all_simplify)
% 2.41/2.69  (step t403 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule cong :premises (t401 t402))
% 2.41/2.69  (step t404 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t405)
% 2.41/2.69  (assume t405.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t405.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (:= Y (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.41/2.69  (step t405.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule or :premises (t405.t1))
% 2.41/2.69  (step t405.t3 (cl (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t405.t2 t405.a0))
% 2.41/2.69  (step t405 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule subproof :discharge (t405.a0))
% 2.41/2.69  (step t406 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t404 t405))
% 2.41/2.69  (step t407 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule implies_neg2)
% 2.41/2.69  (step t408 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule resolution :premises (t406 t407))
% 2.41/2.69  (step t409 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule contraction :premises (t408))
% 2.41/2.69  (step t410 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t400 t403 t409))
% 2.41/2.69  (step t411 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies :premises (t410))
% 2.41/2.69  (step t412 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (tptp.and (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t411 a9))
% 2.41/2.69  (step t413 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule equiv_pos2)
% 2.41/2.69  (step t414 (cl (= (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule all_simplify)
% 2.41/2.69  (step t415 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule cong :premises (t401 t414))
% 2.41/2.69  (step t416 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t417)
% 2.41/2.69  (assume t417.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t417.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (:= Y (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))
% 2.41/2.69  (step t417.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule or :premises (t417.t1))
% 2.41/2.69  (step t417.t3 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule resolution :premises (t417.t2 t417.a0))
% 2.41/2.69  (step t417 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule subproof :discharge (t417.a0))
% 2.41/2.69  (step t418 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule resolution :premises (t416 t417))
% 2.41/2.69  (step t419 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t420 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t418 t419))
% 2.41/2.69  (step t421 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule contraction :premises (t420))
% 2.41/2.69  (step t422 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule resolution :premises (t413 t415 t421))
% 2.41/2.69  (step t423 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule implies :premises (t422))
% 2.41/2.69  (step t424 (cl (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule resolution :premises (t423 a9))
% 2.41/2.69  (step t425 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule equiv_pos2)
% 2.41/2.69  (step t426 (cl (= (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth)) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule all_simplify)
% 2.41/2.69  (step t427 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule cong :premises (t401 t426))
% 2.41/2.69  (step t428 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t429)
% 2.41/2.69  (assume t429.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t429.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))
% 2.41/2.69  (step t429.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth))) :rule or :premises (t429.t1))
% 2.41/2.69  (step t429.t3 (cl (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth))) :rule resolution :premises (t429.t2 t429.a0))
% 2.41/2.69  (step t429 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth))) :rule subproof :discharge (t429.a0))
% 2.41/2.69  (step t430 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth))) :rule resolution :premises (t428 t429))
% 2.41/2.69  (step t431 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth))) (not (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth)))) :rule implies_neg2)
% 2.41/2.69  (step t432 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth)))) :rule resolution :premises (t430 t431))
% 2.41/2.69  (step t433 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth)))) :rule contraction :premises (t432))
% 2.41/2.69  (step t434 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t425 t427 t433))
% 2.41/2.69  (step t435 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule implies :premises (t434))
% 2.41/2.69  (step t436 (cl (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t435 a9))
% 2.41/2.69  (step t437 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))))) :rule equiv_pos2)
% 2.41/2.69  (step t438 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))) :rule refl)
% 2.41/2.69  (step t439 (cl (= (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x)))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))))) :rule all_simplify)
% 2.41/2.69  (step t440 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))))) :rule cong :premises (t438 t439))
% 2.41/2.69  (step t441 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t442)
% 2.41/2.69  (assume t442.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.69  (step t442.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x)))))) :rule forall_inst :args ((:= X (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (:= Y tptp.x) (:= Z (tptp.not tptp.x))))
% 2.41/2.69  (step t442.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))))) :rule or :premises (t442.t1))
% 2.41/2.69  (step t442.t3 (cl (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))))) :rule resolution :premises (t442.t2 t442.a0))
% 2.41/2.69  (step t442 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))))) :rule subproof :discharge (t442.a0))
% 2.41/2.69  (step t443 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))))) :rule resolution :premises (t441 t442))
% 2.41/2.69  (step t444 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))))) (not (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x)))))) :rule implies_neg2)
% 2.41/2.69  (step t445 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x)))))) :rule resolution :premises (t443 t444))
% 2.41/2.69  (step t446 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x)))))) :rule contraction :premises (t445))
% 2.41/2.69  (step t447 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x))))) :rule resolution :premises (t437 t440 t446))
% 2.41/2.69  (step t448 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))) :rule implies :premises (t447))
% 2.41/2.69  (step t449 (cl (= (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not tptp.x))) (tptp.and (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.x))) tptp.x) (tptp.not tptp.x)))) :rule resolution :premises (t448 a8))
% 2.41/2.69  (step t450 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t451)
% 2.41/2.69  (assume t451.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.69  (step t451.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))))) :rule forall_inst :args ((:= X tptp.truth) (:= Y tptp.falsehood) (:= Z tptp.x)))
% 2.41/2.69  (step t451.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) :rule or :premises (t451.t1))
% 2.41/2.69  (step t451.t3 (cl (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) :rule resolution :premises (t451.t2 t451.a0))
% 2.41/2.69  (step t451 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) :rule subproof :discharge (t451.a0))
% 2.41/2.69  (step t452 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) :rule resolution :premises (t450 t451))
% 2.41/2.69  (step t453 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))))) :rule implies_neg2)
% 2.41/2.69  (step t454 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))))) :rule resolution :premises (t452 t453))
% 2.41/2.69  (step t455 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x))))) :rule contraction :premises (t454))
% 2.41/2.69  (step t456 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) :rule implies :premises (t455))
% 2.41/2.69  (step t457 (cl (= (tptp.and (tptp.and tptp.truth tptp.falsehood) tptp.x) (tptp.and tptp.truth (tptp.and tptp.falsehood tptp.x)))) :rule resolution :premises (t456 a8))
% 2.41/2.69  (step t458 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t459)
% 2.41/2.69  (assume t459.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.69  (step t459.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))))) :rule forall_inst :args ((:= X tptp.x) (:= Y (tptp.not tptp.x)) (:= Z (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))
% 2.41/2.69  (step t459.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) :rule or :premises (t459.t1))
% 2.41/2.69  (step t459.t3 (cl (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) :rule resolution :premises (t459.t2 t459.a0))
% 2.41/2.69  (step t459 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) :rule subproof :discharge (t459.a0))
% 2.41/2.69  (step t460 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) :rule resolution :premises (t458 t459))
% 2.41/2.69  (step t461 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))))) :rule implies_neg2)
% 2.41/2.69  (step t462 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))))) :rule resolution :premises (t460 t461))
% 2.41/2.69  (step t463 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))))))) :rule contraction :premises (t462))
% 2.41/2.69  (step t464 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) :rule implies :premises (t463))
% 2.41/2.69  (step t465 (cl (= (tptp.and (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.and tptp.x (tptp.not tptp.x)))) (tptp.and tptp.x (tptp.and (tptp.not tptp.x) (tptp.not (tptp.and tptp.x (tptp.not tptp.x))))))) :rule resolution :premises (t464 a8))
% 2.41/2.69  (step t466 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t467)
% 2.41/2.69  (assume t467.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.69  (step t467.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule forall_inst :args ((:= X tptp.x) (:= Y tptp.falsehood) (:= Z (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))
% 2.41/2.69  (step t467.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule or :premises (t467.t1))
% 2.41/2.69  (step t467.t3 (cl (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule resolution :premises (t467.t2 t467.a0))
% 2.41/2.69  (step t467 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule subproof :discharge (t467.a0))
% 2.41/2.69  (step t468 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule resolution :premises (t466 t467))
% 2.41/2.69  (step t469 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule implies_neg2)
% 2.41/2.69  (step t470 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule resolution :premises (t468 t469))
% 2.41/2.69  (step t471 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule contraction :premises (t470))
% 2.41/2.69  (step t472 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule implies :premises (t471))
% 2.41/2.69  (step t473 (cl (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule resolution :premises (t472 a8))
% 2.41/2.69  (step t474 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t475)
% 2.41/2.69  (assume t475.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t475.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (:= Y (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.41/2.69  (step t475.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule or :premises (t475.t1))
% 2.41/2.69  (step t475.t3 (cl (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t475.t2 t475.a0))
% 2.41/2.69  (step t475 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule subproof :discharge (t475.a0))
% 2.41/2.69  (step t476 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t474 t475))
% 2.41/2.69  (step t477 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule implies_neg2)
% 2.41/2.69  (step t478 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t476 t477))
% 2.41/2.69  (step t479 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule contraction :premises (t478))
% 2.41/2.69  (step t480 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies :premises (t479))
% 2.41/2.69  (step t481 (cl (= (tptp.and (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t480 a7))
% 2.41/2.69  (step t482 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t483)
% 2.41/2.69  (assume t483.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t483.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))
% 2.41/2.69  (step t483.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule or :premises (t483.t1))
% 2.41/2.69  (step t483.t3 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule resolution :premises (t483.t2 t483.a0))
% 2.41/2.69  (step t483 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule subproof :discharge (t483.a0))
% 2.41/2.69  (step t484 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule resolution :premises (t482 t483))
% 2.41/2.69  (step t485 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule implies_neg2)
% 2.41/2.69  (step t486 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule resolution :premises (t484 t485))
% 2.41/2.69  (step t487 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule contraction :premises (t486))
% 2.41/2.69  (step t488 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule implies :premises (t487))
% 2.41/2.69  (step t489 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))) :rule resolution :premises (t488 a7))
% 2.41/2.69  (step t490 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t491)
% 2.41/2.69  (assume t491.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t491.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y tptp.x)))
% 2.41/2.69  (step t491.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) :rule or :premises (t491.t1))
% 2.41/2.69  (step t491.t3 (cl (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) :rule resolution :premises (t491.t2 t491.a0))
% 2.41/2.69  (step t491 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) :rule subproof :discharge (t491.a0))
% 2.41/2.69  (step t492 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) :rule resolution :premises (t490 t491))
% 2.41/2.69  (step t493 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))))) :rule implies_neg2)
% 2.41/2.69  (step t494 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))))) :rule resolution :premises (t492 t493))
% 2.41/2.69  (step t495 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x)))))) :rule contraction :premises (t494))
% 2.41/2.69  (step t496 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) :rule implies :premises (t495))
% 2.41/2.69  (step t497 (cl (= (tptp.and (tptp.not tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.x))))) :rule resolution :premises (t496 a7))
% 2.41/2.69  (step t498 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t499)
% 2.41/2.69  (assume t499.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t499.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (:= Y (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))
% 2.41/2.69  (step t499.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule or :premises (t499.t1))
% 2.41/2.69  (step t499.t3 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule resolution :premises (t499.t2 t499.a0))
% 2.41/2.69  (step t499 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule subproof :discharge (t499.a0))
% 2.41/2.69  (step t500 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule resolution :premises (t498 t499))
% 2.41/2.69  (step t501 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule implies_neg2)
% 2.41/2.69  (step t502 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule resolution :premises (t500 t501))
% 2.41/2.69  (step t503 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))))))))) :rule contraction :premises (t502))
% 2.41/2.69  (step t504 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule implies :premises (t503))
% 2.41/2.69  (step t505 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))))) :rule resolution :premises (t504 a7))
% 2.41/2.69  (step t506 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t507)
% 2.41/2.69  (assume t507.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t507.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) :rule forall_inst :args ((:= X (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (:= Y tptp.truth)))
% 2.41/2.69  (step t507.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule or :premises (t507.t1))
% 2.41/2.69  (step t507.t3 (cl (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule resolution :premises (t507.t2 t507.a0))
% 2.41/2.69  (step t507 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule subproof :discharge (t507.a0))
% 2.41/2.69  (step t508 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule resolution :premises (t506 t507))
% 2.41/2.69  (step t509 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) :rule implies_neg2)
% 2.41/2.69  (step t510 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) :rule resolution :premises (t508 t509))
% 2.41/2.69  (step t511 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth)))))) :rule contraction :premises (t510))
% 2.41/2.69  (step t512 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule implies :premises (t511))
% 2.41/2.69  (step t513 (cl (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.truth))))) :rule resolution :premises (t512 a7))
% 2.41/2.69  (step t514 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t515)
% 2.41/2.69  (assume t515.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t515.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))))) :rule forall_inst :args ((:= X tptp.x) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t515.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) :rule or :premises (t515.t1))
% 2.41/2.69  (step t515.t3 (cl (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t515.t2 t515.a0))
% 2.41/2.69  (step t515 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) :rule subproof :discharge (t515.a0))
% 2.41/2.69  (step t516 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t514 t515))
% 2.41/2.69  (step t517 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))))) :rule implies_neg2)
% 2.41/2.69  (step t518 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))))) :rule resolution :premises (t516 t517))
% 2.41/2.69  (step t519 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))))) :rule contraction :premises (t518))
% 2.41/2.69  (step t520 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) :rule implies :premises (t519))
% 2.41/2.69  (step t521 (cl (= (tptp.and tptp.x (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t520 a7))
% 2.41/2.69  (step t522 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t523)
% 2.41/2.69  (assume t523.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t523.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))
% 2.41/2.69  (step t523.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule or :premises (t523.t1))
% 2.41/2.69  (step t523.t3 (cl (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t523.t2 t523.a0))
% 2.41/2.69  (step t523 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule subproof :discharge (t523.a0))
% 2.41/2.69  (step t524 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t522 t523))
% 2.41/2.69  (step t525 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule implies_neg2)
% 2.41/2.69  (step t526 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule resolution :premises (t524 t525))
% 2.41/2.69  (step t527 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule contraction :premises (t526))
% 2.41/2.69  (step t528 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule implies :premises (t527))
% 2.41/2.69  (step t529 (cl (= (tptp.and tptp.truth (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t528 a7))
% 2.41/2.69  (step t530 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t531)
% 2.41/2.69  (assume t531.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t531.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not (tptp.not tptp.x)))) (:= Y (tptp.not (tptp.not tptp.falsehood)))))
% 2.41/2.69  (step t531.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule or :premises (t531.t1))
% 2.41/2.69  (step t531.t3 (cl (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t531.t2 t531.a0))
% 2.41/2.69  (step t531 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule subproof :discharge (t531.a0))
% 2.41/2.69  (step t532 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t530 t531))
% 2.41/2.69  (step t533 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule implies_neg2)
% 2.41/2.69  (step t534 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t532 t533))
% 2.41/2.69  (step t535 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule contraction :premises (t534))
% 2.41/2.69  (step t536 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule implies :premises (t535))
% 2.41/2.69  (step t537 (cl (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t536 a6))
% 2.41/2.69  (step t538 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule equiv_pos2)
% 2.41/2.69  (step t539 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))) :rule refl)
% 2.41/2.69  (step t540 (cl (= (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule all_simplify)
% 2.41/2.69  (step t541 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) :rule cong :premises (t539 t540))
% 2.41/2.69  (step t542 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t543)
% 2.41/2.69  (assume t543.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t543.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t543.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule or :premises (t543.t1))
% 2.41/2.69  (step t543.t3 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t543.t2 t543.a0))
% 2.41/2.69  (step t543 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule subproof :discharge (t543.a0))
% 2.41/2.69  (step t544 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t542 t543))
% 2.41/2.69  (step t545 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies_neg2)
% 2.41/2.69  (step t546 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t544 t545))
% 2.41/2.69  (step t547 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule contraction :premises (t546))
% 2.41/2.69  (step t548 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule resolution :premises (t538 t541 t547))
% 2.41/2.69  (step t549 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) :rule implies :premises (t548))
% 2.41/2.69  (step t550 (cl (= (tptp.or (tptp.not tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))) :rule resolution :premises (t549 a6))
% 2.41/2.69  (step t551 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t552)
% 2.41/2.69  (assume t552.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t552.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y (tptp.not tptp.x))))
% 2.41/2.69  (step t552.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) :rule or :premises (t552.t1))
% 2.41/2.69  (step t552.t3 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) :rule resolution :premises (t552.t2 t552.a0))
% 2.41/2.69  (step t552 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) :rule subproof :discharge (t552.a0))
% 2.41/2.69  (step t553 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) :rule resolution :premises (t551 t552))
% 2.41/2.69  (step t554 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)))) :rule implies_neg2)
% 2.41/2.69  (step t555 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)))) :rule resolution :premises (t553 t554))
% 2.41/2.69  (step t556 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood)))) :rule contraction :premises (t555))
% 2.41/2.69  (step t557 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) :rule implies :premises (t556))
% 2.41/2.69  (step t558 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.falsehood))) :rule resolution :premises (t557 a6))
% 2.41/2.69  (step t559 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule equiv_pos2)
% 2.41/2.69  (step t560 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))) :rule refl)
% 2.41/2.69  (step t561 (cl (= (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule all_simplify)
% 2.41/2.69  (step t562 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))))) :rule cong :premises (t560 t561))
% 2.41/2.69  (step t563 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t564)
% 2.41/2.69  (assume t564.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t564.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.41/2.69  (step t564.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule or :premises (t564.t1))
% 2.41/2.69  (step t564.t3 (cl (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t564.t2 t564.a0))
% 2.41/2.69  (step t564 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule subproof :discharge (t564.a0))
% 2.41/2.69  (step t565 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t563 t564))
% 2.41/2.69  (step t566 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule implies_neg2)
% 2.41/2.69  (step t567 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t565 t566))
% 2.41/2.69  (step t568 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule contraction :premises (t567))
% 2.41/2.69  (step t569 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t559 t562 t568))
% 2.41/2.69  (step t570 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))) :rule implies :premises (t569))
% 2.41/2.69  (step t571 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.or tptp.falsehood (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t570 a4))
% 2.41/2.69  (step t572 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)))) :rule equiv_pos2)
% 2.41/2.69  (step t573 (cl (= (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood)) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)))) :rule all_simplify)
% 2.41/2.69  (step t574 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))))) :rule cong :premises (t560 t573))
% 2.41/2.69  (step t575 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t576)
% 2.41/2.69  (assume t576.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t576.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood)))) :rule forall_inst :args ((:= X tptp.x) (:= Y tptp.falsehood)))
% 2.41/2.69  (step t576.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood))) :rule or :premises (t576.t1))
% 2.41/2.69  (step t576.t3 (cl (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood))) :rule resolution :premises (t576.t2 t576.a0))
% 2.41/2.69  (step t576 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood))) :rule subproof :discharge (t576.a0))
% 2.41/2.69  (step t577 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood))) :rule resolution :premises (t575 t576))
% 2.41/2.69  (step t578 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood))) (not (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood)))) :rule implies_neg2)
% 2.41/2.69  (step t579 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood)))) :rule resolution :premises (t577 t578))
% 2.41/2.69  (step t580 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.x tptp.falsehood) (tptp.implies (tptp.not tptp.x) tptp.falsehood)))) :rule contraction :premises (t579))
% 2.41/2.69  (step t581 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood)))) :rule resolution :premises (t572 t574 t580))
% 2.41/2.69  (step t582 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))) :rule implies :premises (t581))
% 2.41/2.69  (step t583 (cl (= (tptp.implies (tptp.not tptp.x) tptp.falsehood) (tptp.or tptp.x tptp.falsehood))) :rule resolution :premises (t582 a4))
% 2.41/2.69  (step t584 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t585)
% 2.41/2.69  (assume t585.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t585.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not tptp.falsehood))) (:= Y (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.41/2.69  (step t585.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule or :premises (t585.t1))
% 2.41/2.69  (step t585.t3 (cl (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t585.t2 t585.a0))
% 2.41/2.69  (step t585 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule subproof :discharge (t585.a0))
% 2.41/2.69  (step t586 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t584 t585))
% 2.41/2.69  (step t587 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule implies_neg2)
% 2.41/2.69  (step t588 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t586 t587))
% 2.41/2.69  (step t589 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule contraction :premises (t588))
% 2.41/2.69  (step t590 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule implies :premises (t589))
% 2.41/2.69  (step t591 (cl (= (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t590 a4))
% 2.41/2.69  (step t592 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t593)
% 2.41/2.69  (assume t593.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t593.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not (tptp.not tptp.x)))) (:= Y (tptp.not (tptp.not tptp.falsehood)))))
% 2.41/2.69  (step t593.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) :rule or :premises (t593.t1))
% 2.41/2.69  (step t593.t3 (cl (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) :rule resolution :premises (t593.t2 t593.a0))
% 2.41/2.69  (step t593 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) :rule subproof :discharge (t593.a0))
% 2.41/2.69  (step t594 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) :rule resolution :premises (t592 t593))
% 2.41/2.69  (step t595 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t596 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t594 t595))
% 2.41/2.69  (step t597 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood)))))) :rule contraction :premises (t596))
% 2.41/2.69  (step t598 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) :rule implies :premises (t597))
% 2.41/2.69  (step t599 (cl (= (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.not tptp.falsehood))))) :rule resolution :premises (t598 a4))
% 2.41/2.69  (step t600 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t601)
% 2.41/2.69  (assume t601.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t601.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule forall_inst :args ((:= X (tptp.not tptp.x)) (:= Y (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))
% 2.41/2.69  (step t601.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule or :premises (t601.t1))
% 2.41/2.69  (step t601.t3 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t601.t2 t601.a0))
% 2.41/2.69  (step t601 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule subproof :discharge (t601.a0))
% 2.41/2.69  (step t602 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t600 t601))
% 2.41/2.69  (step t603 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule implies_neg2)
% 2.41/2.69  (step t604 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule resolution :premises (t602 t603))
% 2.41/2.69  (step t605 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule contraction :premises (t604))
% 2.41/2.69  (step t606 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule implies :premises (t605))
% 2.41/2.69  (step t607 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t606 a4))
% 2.41/2.69  (step t608 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t609)
% 2.41/2.69  (assume t609.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t609.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))))) :rule forall_inst :args ((:= X (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t609.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) :rule or :premises (t609.t1))
% 2.41/2.69  (step t609.t3 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) :rule resolution :premises (t609.t2 t609.a0))
% 2.41/2.69  (step t609 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) :rule subproof :discharge (t609.a0))
% 2.41/2.69  (step t610 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) :rule resolution :premises (t608 t609))
% 2.41/2.69  (step t611 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))))) :rule implies_neg2)
% 2.41/2.69  (step t612 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))))) :rule resolution :premises (t610 t611))
% 2.41/2.69  (step t613 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood))))) :rule contraction :premises (t612))
% 2.41/2.69  (step t614 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) :rule implies :premises (t613))
% 2.41/2.69  (step t615 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not tptp.falsehood)))) :rule resolution :premises (t614 a4))
% 2.41/2.69  (step t616 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t617)
% 2.41/2.69  (assume t617.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))))
% 2.41/2.69  (step t617.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y tptp.truth)))
% 2.41/2.69  (step t617.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule or :premises (t617.t1))
% 2.41/2.69  (step t617.t3 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule resolution :premises (t617.t2 t617.a0))
% 2.41/2.69  (step t617 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule subproof :discharge (t617.a0))
% 2.41/2.69  (step t618 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule resolution :premises (t616 t617))
% 2.41/2.69  (step t619 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t620 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))))) :rule resolution :premises (t618 t619))
% 2.41/2.69  (step t621 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))))) :rule contraction :premises (t620))
% 2.41/2.69  (step t622 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule implies :premises (t621))
% 2.41/2.69  (step t623 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule resolution :premises (t622 t350))
% 2.41/2.69  (step t624 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t625)
% 2.41/2.69  (assume t625.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 2.41/2.69  (step t625.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y (tptp.not (tptp.not tptp.x)))))
% 2.41/2.69  (step t625.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule or :premises (t625.t1))
% 2.41/2.69  (step t625.t3 (cl (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule resolution :premises (t625.t2 t625.a0))
% 2.41/2.69  (step t625 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule subproof :discharge (t625.a0))
% 2.41/2.69  (step t626 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule resolution :premises (t624 t625))
% 2.41/2.69  (step t627 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule implies_neg2)
% 2.41/2.69  (step t628 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule resolution :premises (t626 t627))
% 2.41/2.69  (step t629 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule contraction :premises (t628))
% 2.41/2.69  (step t630 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule implies :premises (t629))
% 2.41/2.69  (step t631 (cl (= (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule resolution :premises (t630 a2))
% 2.41/2.69  (step t632 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t633)
% 2.41/2.69  (assume t633.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 2.41/2.69  (step t633.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (:= Y tptp.truth)))
% 2.41/2.69  (step t633.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule or :premises (t633.t1))
% 2.41/2.69  (step t633.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule resolution :premises (t633.t2 t633.a0))
% 2.41/2.69  (step t633 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule subproof :discharge (t633.a0))
% 2.41/2.69  (step t634 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule resolution :premises (t632 t633))
% 2.41/2.69  (step t635 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t636 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))))) :rule resolution :premises (t634 t635))
% 2.41/2.69  (step t637 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))))) :rule contraction :premises (t636))
% 2.41/2.69  (step t638 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule implies :premises (t637))
% 2.41/2.69  (step t639 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) tptp.truth) tptp.truth) (tptp.implies (tptp.implies tptp.truth (tptp.implies tptp.truth (tptp.not tptp.falsehood))) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule resolution :premises (t638 a2))
% 2.41/2.69  (step t640 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t641)
% 2.41/2.69  (assume t641.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 2.41/2.69  (step t641.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t641.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) :rule or :premises (t641.t1))
% 2.41/2.69  (step t641.t3 (cl (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) :rule resolution :premises (t641.t2 t641.a0))
% 2.41/2.69  (step t641 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) :rule subproof :discharge (t641.a0))
% 2.41/2.69  (step t642 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) :rule resolution :premises (t640 t641))
% 2.41/2.69  (step t643 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (not (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule implies_neg2)
% 2.41/2.69  (step t644 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule resolution :premises (t642 t643))
% 2.41/2.69  (step t645 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood))))) :rule contraction :premises (t644))
% 2.41/2.69  (step t646 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) :rule implies :premises (t645))
% 2.41/2.69  (step t647 (cl (= (tptp.not tptp.falsehood) (tptp.implies tptp.truth (tptp.not tptp.falsehood)))) :rule resolution :premises (t646 t162))
% 2.41/2.69  (step t648 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t649)
% 2.41/2.69  (assume t649.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 2.41/2.69  (step t649.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not tptp.x)))))
% 2.41/2.69  (step t649.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) :rule or :premises (t649.t1))
% 2.41/2.69  (step t649.t3 (cl (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) :rule resolution :premises (t649.t2 t649.a0))
% 2.41/2.69  (step t649 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) :rule subproof :discharge (t649.a0))
% 2.41/2.69  (step t650 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) :rule resolution :premises (t648 t649))
% 2.41/2.69  (step t651 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (not (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule implies_neg2)
% 2.41/2.69  (step t652 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t650 t651))
% 2.41/2.69  (step t653 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule contraction :premises (t652))
% 2.41/2.69  (step t654 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) :rule implies :premises (t653))
% 2.41/2.69  (step t655 (cl (= (tptp.not (tptp.not tptp.x)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))) :rule resolution :premises (t654 t162))
% 2.41/2.69  (step t656 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.x (tptp.implies tptp.truth tptp.x))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t657)
% 2.41/2.69  (assume t657.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 2.41/2.69  (step t657.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.x (tptp.implies tptp.truth tptp.x)))) :rule forall_inst :args ((:= X tptp.x)))
% 2.41/2.69  (step t657.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.x (tptp.implies tptp.truth tptp.x))) :rule or :premises (t657.t1))
% 2.41/2.69  (step t657.t3 (cl (= tptp.x (tptp.implies tptp.truth tptp.x))) :rule resolution :premises (t657.t2 t657.a0))
% 2.41/2.69  (step t657 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.x (tptp.implies tptp.truth tptp.x))) :rule subproof :discharge (t657.a0))
% 2.41/2.69  (step t658 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.x (tptp.implies tptp.truth tptp.x))) (= tptp.x (tptp.implies tptp.truth tptp.x))) :rule resolution :premises (t656 t657))
% 2.41/2.69  (step t659 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.x (tptp.implies tptp.truth tptp.x))) (not (= tptp.x (tptp.implies tptp.truth tptp.x)))) :rule implies_neg2)
% 2.41/2.69  (step t660 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.x (tptp.implies tptp.truth tptp.x))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.x (tptp.implies tptp.truth tptp.x)))) :rule resolution :premises (t658 t659))
% 2.41/2.69  (step t661 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.x (tptp.implies tptp.truth tptp.x)))) :rule contraction :premises (t660))
% 2.41/2.69  (step t662 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.x (tptp.implies tptp.truth tptp.x))) :rule implies :premises (t661))
% 2.41/2.69  (step t663 (cl (= tptp.x (tptp.implies tptp.truth tptp.x))) :rule resolution :premises (t662 t162))
% 2.41/2.69  (step t664 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t665)
% 2.41/2.69  (assume t665.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t665.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (:= Y tptp.falsehood)))
% 2.41/2.69  (step t665.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule or :premises (t665.t1))
% 2.41/2.69  (step t665.t3 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule resolution :premises (t665.t2 t665.a0))
% 2.41/2.69  (step t665 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule subproof :discharge (t665.a0))
% 2.41/2.69  (step t666 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule resolution :premises (t664 t665))
% 2.41/2.69  (step t667 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t668 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t666 t667))
% 2.41/2.69  (step t669 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule contraction :premises (t668))
% 2.41/2.69  (step t670 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule implies :premises (t669))
% 2.41/2.69  (step t671 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule resolution :premises (t670 a9))
% 2.41/2.69  (step t672 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t673)
% 2.41/2.69  (assume t673.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t673.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule forall_inst :args ((:= X (tptp.and tptp.x (tptp.not tptp.truth))) (:= Y (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))))))
% 2.41/2.69  (step t673.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule or :premises (t673.t1))
% 2.41/2.69  (step t673.t3 (cl (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t673.t2 t673.a0))
% 2.41/2.69  (step t673 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule subproof :discharge (t673.a0))
% 2.41/2.69  (step t674 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t672 t673))
% 2.41/2.69  (step t675 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule implies_neg2)
% 2.41/2.69  (step t676 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t674 t675))
% 2.41/2.69  (step t677 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule contraction :premises (t676))
% 2.41/2.69  (step t678 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule implies :premises (t677))
% 2.41/2.69  (step t679 (cl (= (tptp.and (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.not (tptp.and tptp.x (tptp.not tptp.truth)))) (tptp.and (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t678 a9))
% 2.41/2.69  (step t680 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule equiv_pos2)
% 2.41/2.69  (step t681 (cl (= (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x)) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule all_simplify)
% 2.41/2.69  (step t682 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule cong :premises (t401 t681))
% 2.41/2.69  (step t683 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t684)
% 2.41/2.69  (assume t684.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t684.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x)))) :rule forall_inst :args ((:= X tptp.x) (:= Y (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.41/2.69  (step t684.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x))) :rule or :premises (t684.t1))
% 2.41/2.69  (step t684.t3 (cl (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x))) :rule resolution :premises (t684.t2 t684.a0))
% 2.41/2.69  (step t684 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x))) :rule subproof :discharge (t684.a0))
% 2.41/2.69  (step t685 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x))) :rule resolution :premises (t683 t684))
% 2.41/2.69  (step t686 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x))) (not (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x)))) :rule implies_neg2)
% 2.41/2.69  (step t687 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x)))) :rule resolution :premises (t685 t686))
% 2.41/2.69  (step t688 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x)))) :rule contraction :premises (t687))
% 2.41/2.69  (step t689 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t680 t682 t688))
% 2.41/2.69  (step t690 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule implies :premises (t689))
% 2.41/2.69  (step t691 (cl (= (tptp.and (tptp.not (tptp.not (tptp.not tptp.x))) tptp.x) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t690 a9))
% 2.41/2.69  (step t692 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))))) :rule equiv_pos2)
% 2.41/2.69  (step t693 (cl (= (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth)) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))))) :rule all_simplify)
% 2.41/2.69  (step t694 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))))) :rule cong :premises (t401 t693))
% 2.41/2.69  (step t695 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t696)
% 2.41/2.69  (assume t696.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t696.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t696.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth))) :rule or :premises (t696.t1))
% 2.41/2.69  (step t696.t3 (cl (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth))) :rule resolution :premises (t696.t2 t696.a0))
% 2.41/2.69  (step t696 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth))) :rule subproof :discharge (t696.a0))
% 2.41/2.69  (step t697 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth))) :rule resolution :premises (t695 t696))
% 2.41/2.69  (step t698 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth))) (not (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth)))) :rule implies_neg2)
% 2.41/2.69  (step t699 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth)))) :rule resolution :premises (t697 t698))
% 2.41/2.69  (step t700 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.truth)))) :rule contraction :premises (t699))
% 2.41/2.69  (step t701 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood))))) :rule resolution :premises (t692 t694 t700))
% 2.41/2.69  (step t702 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))) :rule implies :premises (t701))
% 2.41/2.69  (step t703 (cl (= (tptp.and (tptp.not tptp.falsehood) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.falsehood)))) :rule resolution :premises (t702 a9))
% 2.41/2.69  (step t704 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) :rule equiv_pos2)
% 2.41/2.69  (step t705 (cl (= (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) :rule all_simplify)
% 2.41/2.69  (step t706 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))))) :rule cong :premises (t401 t705))
% 2.41/2.69  (step t707 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t708)
% 2.41/2.69  (assume t708.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t708.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.not (tptp.not tptp.falsehood)))))
% 2.41/2.69  (step t708.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) :rule or :premises (t708.t1))
% 2.41/2.69  (step t708.t3 (cl (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) :rule resolution :premises (t708.t2 t708.a0))
% 2.41/2.69  (step t708 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) :rule subproof :discharge (t708.a0))
% 2.41/2.69  (step t709 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) :rule resolution :premises (t707 t708))
% 2.41/2.69  (step t710 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (not (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule implies_neg2)
% 2.41/2.69  (step t711 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule resolution :premises (t709 t710))
% 2.41/2.69  (step t712 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule contraction :premises (t711))
% 2.41/2.69  (step t713 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t704 t706 t712))
% 2.41/2.69  (step t714 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) :rule implies :premises (t713))
% 2.41/2.69  (step t715 (cl (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))) :rule resolution :premises (t714 a9))
% 2.41/2.69  (step t716 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t717)
% 2.41/2.69  (assume t717.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.69  (step t717.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (:= Y tptp.x) (:= Z tptp.falsehood)))
% 2.41/2.69  (step t717.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) :rule or :premises (t717.t1))
% 2.41/2.69  (step t717.t3 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) :rule resolution :premises (t717.t2 t717.a0))
% 2.41/2.69  (step t717 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) :rule subproof :discharge (t717.a0))
% 2.41/2.69  (step t718 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) :rule resolution :premises (t716 t717))
% 2.41/2.69  (step t719 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))))) :rule implies_neg2)
% 2.41/2.69  (step t720 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))))) :rule resolution :premises (t718 t719))
% 2.41/2.69  (step t721 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood))))) :rule contraction :premises (t720))
% 2.41/2.69  (step t722 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) :rule implies :premises (t721))
% 2.41/2.69  (step t723 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.x) tptp.falsehood) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.x tptp.falsehood)))) :rule resolution :premises (t722 a8))
% 2.41/2.69  (step t724 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t725)
% 2.41/2.69  (assume t725.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.69  (step t725.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule forall_inst :args ((:= X tptp.x) (:= Y tptp.falsehood) (:= Z (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.41/2.69  (step t725.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule or :premises (t725.t1))
% 2.41/2.69  (step t725.t3 (cl (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t725.t2 t725.a0))
% 2.41/2.69  (step t725 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule subproof :discharge (t725.a0))
% 2.41/2.69  (step t726 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t724 t725))
% 2.41/2.69  (step t727 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies_neg2)
% 2.41/2.69  (step t728 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t726 t727))
% 2.41/2.69  (step t729 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule contraction :premises (t728))
% 2.41/2.69  (step t730 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule implies :premises (t729))
% 2.41/2.69  (step t731 (cl (= (tptp.and (tptp.and tptp.x tptp.falsehood) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x (tptp.and tptp.falsehood (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t730 a8))
% 2.41/2.69  (step t732 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t733)
% 2.41/2.69  (assume t733.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t733.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (:= Y (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))
% 2.41/2.69  (step t733.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) :rule or :premises (t733.t1))
% 2.41/2.69  (step t733.t3 (cl (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) :rule resolution :premises (t733.t2 t733.a0))
% 2.41/2.69  (step t733 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) :rule subproof :discharge (t733.a0))
% 2.41/2.69  (step t734 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) :rule resolution :premises (t732 t733))
% 2.41/2.69  (step t735 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) (not (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))))) :rule implies_neg2)
% 2.41/2.69  (step t736 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))))) :rule resolution :premises (t734 t735))
% 2.41/2.69  (step t737 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))))) :rule contraction :premises (t736))
% 2.41/2.69  (step t738 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) :rule implies :premises (t737))
% 2.41/2.69  (step t739 (cl (= (tptp.and (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))))) :rule resolution :premises (t738 a7))
% 2.41/2.69  (step t740 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t741)
% 2.41/2.69  (assume t741.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t741.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))))) :rule forall_inst :args ((:= X (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (:= Y tptp.x)))
% 2.41/2.69  (step t741.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) :rule or :premises (t741.t1))
% 2.41/2.69  (step t741.t3 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) :rule resolution :premises (t741.t2 t741.a0))
% 2.41/2.69  (step t741 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) :rule subproof :discharge (t741.a0))
% 2.41/2.69  (step t742 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) :rule resolution :premises (t740 t741))
% 2.41/2.69  (step t743 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))))) :rule implies_neg2)
% 2.41/2.69  (step t744 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))))) :rule resolution :premises (t742 t743))
% 2.41/2.69  (step t745 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x)))))) :rule contraction :premises (t744))
% 2.41/2.69  (step t746 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) :rule implies :premises (t745))
% 2.41/2.69  (step t747 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood)) (tptp.not tptp.x))))) :rule resolution :premises (t746 a7))
% 2.41/2.69  (step t748 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t749)
% 2.41/2.69  (assume t749.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t749.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y (tptp.not (tptp.not tptp.x)))))
% 2.41/2.69  (step t749.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule or :premises (t749.t1))
% 2.41/2.69  (step t749.t3 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t749.t2 t749.a0))
% 2.41/2.69  (step t749 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule subproof :discharge (t749.a0))
% 2.41/2.69  (step t750 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t748 t749))
% 2.41/2.69  (step t751 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule implies_neg2)
% 2.41/2.69  (step t752 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule resolution :premises (t750 t751))
% 2.41/2.69  (step t753 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule contraction :premises (t752))
% 2.41/2.69  (step t754 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule implies :premises (t753))
% 2.41/2.69  (step t755 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t754 a7))
% 2.41/2.69  (step t756 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t757)
% 2.41/2.69  (assume t757.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t757.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (:= Y tptp.falsehood)))
% 2.41/2.69  (step t757.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule or :premises (t757.t1))
% 2.41/2.69  (step t757.t3 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule resolution :premises (t757.t2 t757.a0))
% 2.41/2.69  (step t757 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule subproof :discharge (t757.a0))
% 2.41/2.69  (step t758 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule resolution :premises (t756 t757))
% 2.41/2.69  (step t759 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t760 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t758 t759))
% 2.41/2.69  (step t761 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood)))))) :rule contraction :premises (t760))
% 2.41/2.69  (step t762 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule implies :premises (t761))
% 2.41/2.69  (step t763 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not tptp.falsehood))))) :rule resolution :premises (t762 a7))
% 2.41/2.69  (step t764 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t765)
% 2.41/2.69  (assume t765.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t765.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule forall_inst :args ((:= X tptp.x) (:= Y (tptp.not (tptp.not (tptp.not tptp.x))))))
% 2.41/2.69  (step t765.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule or :premises (t765.t1))
% 2.41/2.69  (step t765.t3 (cl (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule resolution :premises (t765.t2 t765.a0))
% 2.41/2.69  (step t765 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule subproof :discharge (t765.a0))
% 2.41/2.69  (step t766 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule resolution :premises (t764 t765))
% 2.41/2.69  (step t767 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) (not (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule implies_neg2)
% 2.41/2.69  (step t768 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule resolution :premises (t766 t767))
% 2.41/2.69  (step t769 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x))))))))) :rule contraction :premises (t768))
% 2.41/2.69  (step t770 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule implies :premises (t769))
% 2.41/2.69  (step t771 (cl (= (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule resolution :premises (t770 a7))
% 2.41/2.69  (step t772 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t773)
% 2.41/2.69  (assume t773.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t773.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule forall_inst :args ((:= X (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))) (:= Y (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))))
% 2.41/2.69  (step t773.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule or :premises (t773.t1))
% 2.41/2.69  (step t773.t3 (cl (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t773.t2 t773.a0))
% 2.41/2.69  (step t773 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule subproof :discharge (t773.a0))
% 2.41/2.69  (step t774 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t772 t773))
% 2.41/2.69  (step t775 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule implies_neg2)
% 2.41/2.69  (step t776 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule resolution :premises (t774 t775))
% 2.41/2.69  (step t777 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule contraction :premises (t776))
% 2.41/2.69  (step t778 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule implies :premises (t777))
% 2.41/2.69  (step t779 (cl (= (tptp.or (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x)))) (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))) (tptp.or (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and tptp.x (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t778 a6))
% 2.41/2.69  (step t780 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t781)
% 2.41/2.69  (assume t781.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t781.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))))) :rule forall_inst :args ((:= X (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))) (:= Y (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))))
% 2.41/2.69  (step t781.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) :rule or :premises (t781.t1))
% 2.41/2.69  (step t781.t3 (cl (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t781.t2 t781.a0))
% 2.41/2.69  (step t781 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) :rule subproof :discharge (t781.a0))
% 2.41/2.69  (step t782 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t780 t781))
% 2.41/2.69  (step t783 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))))) :rule implies_neg2)
% 2.41/2.69  (step t784 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))))) :rule resolution :premises (t782 t783))
% 2.41/2.69  (step t785 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))))))) :rule contraction :premises (t784))
% 2.41/2.69  (step t786 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) :rule implies :premises (t785))
% 2.41/2.69  (step t787 (cl (= (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)) (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t786 a6))
% 2.41/2.69  (step t788 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t789)
% 2.41/2.69  (assume t789.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t789.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule forall_inst :args ((:= X (tptp.not tptp.x)) (:= Y (tptp.not (tptp.not tptp.x)))))
% 2.41/2.69  (step t789.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule or :premises (t789.t1))
% 2.41/2.69  (step t789.t3 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule resolution :premises (t789.t2 t789.a0))
% 2.41/2.69  (step t789 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule subproof :discharge (t789.a0))
% 2.41/2.69  (step t790 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule resolution :premises (t788 t789))
% 2.41/2.69  (step t791 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule implies_neg2)
% 2.41/2.69  (step t792 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule resolution :premises (t790 t791))
% 2.41/2.69  (step t793 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule contraction :premises (t792))
% 2.41/2.69  (step t794 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule implies :premises (t793))
% 2.41/2.69  (step t795 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule resolution :premises (t794 a6))
% 2.41/2.69  (step t796 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t797)
% 2.41/2.69  (assume t797.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t797.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t797.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) :rule or :premises (t797.t1))
% 2.41/2.69  (step t797.t3 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) :rule resolution :premises (t797.t2 t797.a0))
% 2.41/2.69  (step t797 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) :rule subproof :discharge (t797.a0))
% 2.41/2.69  (step t798 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) :rule resolution :premises (t796 t797))
% 2.41/2.69  (step t799 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)))) :rule implies_neg2)
% 2.41/2.69  (step t800 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)))) :rule resolution :premises (t798 t799))
% 2.41/2.69  (step t801 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood)))) :rule contraction :premises (t800))
% 2.41/2.69  (step t802 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) :rule implies :premises (t801))
% 2.41/2.69  (step t803 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) tptp.falsehood))) :rule resolution :premises (t802 a6))
% 2.41/2.69  (step t804 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) :rule equiv_pos2)
% 2.41/2.69  (step t805 (cl (= (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood)))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) :rule all_simplify)
% 2.41/2.69  (step t806 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))))) :rule cong :premises (t560 t805))
% 2.41/2.69  (step t807 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t808)
% 2.41/2.69  (assume t808.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t808.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X (tptp.not tptp.x)) (:= Y (tptp.not (tptp.not tptp.falsehood)))))
% 2.41/2.69  (step t808.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))))) :rule or :premises (t808.t1))
% 2.41/2.69  (step t808.t3 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))))) :rule resolution :premises (t808.t2 t808.a0))
% 2.41/2.69  (step t808 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))))) :rule subproof :discharge (t808.a0))
% 2.41/2.69  (step t809 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))))) :rule resolution :premises (t807 t808))
% 2.41/2.69  (step t810 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t811 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t809 t810))
% 2.41/2.69  (step t812 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood)))))) :rule contraction :premises (t811))
% 2.41/2.69  (step t813 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t804 t806 t812))
% 2.41/2.69  (step t814 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) :rule implies :premises (t813))
% 2.41/2.69  (step t815 (cl (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.falsehood))))) :rule resolution :premises (t814 a4))
% 2.41/2.69  (step t816 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))))) :rule equiv_pos2)
% 2.41/2.69  (step t817 (cl (= (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))))) :rule all_simplify)
% 2.41/2.69  (step t818 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))))) :rule cong :premises (t560 t817))
% 2.41/2.69  (step t819 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t820)
% 2.41/2.69  (assume t820.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t820.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y (tptp.not tptp.x))))
% 2.41/2.69  (step t820.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule or :premises (t820.t1))
% 2.41/2.69  (step t820.t3 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule resolution :premises (t820.t2 t820.a0))
% 2.41/2.69  (step t820 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule subproof :discharge (t820.a0))
% 2.41/2.69  (step t821 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule resolution :premises (t819 t820))
% 2.41/2.69  (step t822 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule implies_neg2)
% 2.41/2.69  (step t823 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule resolution :premises (t821 t822))
% 2.41/2.69  (step t824 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule contraction :premises (t823))
% 2.41/2.69  (step t825 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x))))) :rule resolution :premises (t816 t818 t824))
% 2.41/2.69  (step t826 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))) :rule implies :premises (t825))
% 2.41/2.69  (step t827 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.x)) (tptp.or tptp.falsehood (tptp.not tptp.x)))) :rule resolution :premises (t826 a4))
% 2.41/2.69  (step t828 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))))) :rule equiv_pos2)
% 2.41/2.69  (step t829 (cl (= (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))))) :rule all_simplify)
% 2.41/2.69  (step t830 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))))) :rule cong :premises (t560 t829))
% 2.41/2.69  (step t831 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t832)
% 2.41/2.69  (assume t832.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t832.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth))))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y (tptp.not tptp.truth))))
% 2.41/2.69  (step t832.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) :rule or :premises (t832.t1))
% 2.41/2.69  (step t832.t3 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) :rule resolution :premises (t832.t2 t832.a0))
% 2.41/2.69  (step t832 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) :rule subproof :discharge (t832.a0))
% 2.41/2.69  (step t833 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) :rule resolution :premises (t831 t832))
% 2.41/2.69  (step t834 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth))))) :rule implies_neg2)
% 2.41/2.69  (step t835 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth))))) :rule resolution :premises (t833 t834))
% 2.41/2.69  (step t836 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.truth)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth))))) :rule contraction :premises (t835))
% 2.41/2.69  (step t837 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth))))) :rule resolution :premises (t828 t830 t836))
% 2.41/2.69  (step t838 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))) :rule implies :premises (t837))
% 2.41/2.69  (step t839 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.or tptp.falsehood (tptp.not tptp.truth)))) :rule resolution :premises (t838 a4))
% 2.41/2.69  (step t840 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t841)
% 2.41/2.69  (assume t841.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t841.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not tptp.truth))) (:= Y (tptp.not tptp.truth))))
% 2.41/2.69  (step t841.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule or :premises (t841.t1))
% 2.41/2.69  (step t841.t3 (cl (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule resolution :premises (t841.t2 t841.a0))
% 2.41/2.69  (step t841 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule subproof :discharge (t841.a0))
% 2.41/2.69  (step t842 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule resolution :premises (t840 t841))
% 2.41/2.69  (step t843 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))))) :rule implies_neg2)
% 2.41/2.69  (step t844 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))))) :rule resolution :premises (t842 t843))
% 2.41/2.69  (step t845 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth))))) :rule contraction :premises (t844))
% 2.41/2.69  (step t846 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule implies :premises (t845))
% 2.41/2.69  (step t847 (cl (= (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.truth))) (tptp.not tptp.truth)))) :rule resolution :premises (t846 a4))
% 2.41/2.69  (step t848 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t849)
% 2.41/2.69  (assume t849.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t849.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)))) :rule forall_inst :args ((:= X (tptp.not tptp.x)) (:= Y tptp.truth)))
% 2.41/2.69  (step t849.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) :rule or :premises (t849.t1))
% 2.41/2.69  (step t849.t3 (cl (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) :rule resolution :premises (t849.t2 t849.a0))
% 2.41/2.69  (step t849 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) :rule subproof :discharge (t849.a0))
% 2.41/2.69  (step t850 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) :rule resolution :premises (t848 t849))
% 2.41/2.69  (step t851 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) (not (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)))) :rule implies_neg2)
% 2.41/2.69  (step t852 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)))) :rule resolution :premises (t850 t851))
% 2.41/2.69  (step t853 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth)))) :rule contraction :premises (t852))
% 2.41/2.69  (step t854 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) :rule implies :premises (t853))
% 2.41/2.69  (step t855 (cl (= (tptp.or (tptp.not tptp.x) tptp.truth) (tptp.implies (tptp.not (tptp.not tptp.x)) tptp.truth))) :rule resolution :premises (t854 a4))
% 2.41/2.69  (step t856 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t857)
% 2.41/2.69  (assume t857.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t857.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (:= Y (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))
% 2.41/2.69  (step t857.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule or :premises (t857.t1))
% 2.41/2.69  (step t857.t3 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t857.t2 t857.a0))
% 2.41/2.69  (step t857 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule subproof :discharge (t857.a0))
% 2.41/2.69  (step t858 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t856 t857))
% 2.41/2.69  (step t859 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule implies_neg2)
% 2.41/2.69  (step t860 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t858 t859))
% 2.41/2.69  (step t861 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule contraction :premises (t860))
% 2.41/2.69  (step t862 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies :premises (t861))
% 2.41/2.69  (step t863 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (tptp.implies (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t862 a4))
% 2.41/2.69  (step t864 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t865)
% 2.41/2.69  (assume t865.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t865.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))))) :rule forall_inst :args ((:= X (tptp.not tptp.truth)) (:= Y (tptp.not (tptp.not tptp.x)))))
% 2.41/2.69  (step t865.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) :rule or :premises (t865.t1))
% 2.41/2.69  (step t865.t3 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) :rule resolution :premises (t865.t2 t865.a0))
% 2.41/2.69  (step t865 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) :rule subproof :discharge (t865.a0))
% 2.41/2.69  (step t866 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) :rule resolution :premises (t864 t865))
% 2.41/2.69  (step t867 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))))) :rule implies_neg2)
% 2.41/2.69  (step t868 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t866 t867))
% 2.41/2.69  (step t869 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x)))))) :rule contraction :premises (t868))
% 2.41/2.69  (step t870 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) :rule implies :premises (t869))
% 2.41/2.69  (step t871 (cl (= (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.truth)) (tptp.not (tptp.not tptp.x))))) :rule resolution :premises (t870 a4))
% 2.41/2.69  (step t872 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t873)
% 2.41/2.69  (assume t873.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))))
% 2.41/2.69  (step t873.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule forall_inst :args ((:= X (tptp.and (tptp.not tptp.x) tptp.truth)) (:= Y (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.41/2.69  (step t873.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule or :premises (t873.t1))
% 2.41/2.69  (step t873.t3 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule resolution :premises (t873.t2 t873.a0))
% 2.41/2.69  (step t873 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule subproof :discharge (t873.a0))
% 2.41/2.69  (step t874 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule resolution :premises (t872 t873))
% 2.41/2.69  (step t875 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule implies_neg2)
% 2.41/2.69  (step t876 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule resolution :premises (t874 t875))
% 2.41/2.69  (step t877 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth)))))) :rule contraction :premises (t876))
% 2.41/2.69  (step t878 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule implies :premises (t877))
% 2.41/2.69  (step t879 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.implies (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule resolution :premises (t878 t350))
% 2.41/2.69  (step t880 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t881)
% 2.41/2.69  (assume t881.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))))
% 2.41/2.69  (step t881.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not tptp.x))) (:= Y tptp.truth)))
% 2.41/2.69  (step t881.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule or :premises (t881.t1))
% 2.41/2.69  (step t881.t3 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t881.t2 t881.a0))
% 2.41/2.69  (step t881 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule subproof :discharge (t881.a0))
% 2.41/2.69  (step t882 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t880 t881))
% 2.41/2.69  (step t883 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))))) :rule implies_neg2)
% 2.41/2.69  (step t884 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t882 t883))
% 2.41/2.69  (step t885 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x))))))) :rule contraction :premises (t884))
% 2.41/2.69  (step t886 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule implies :premises (t885))
% 2.41/2.69  (step t887 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t886 t350))
% 2.41/2.69  (step t888 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t889)
% 2.41/2.69  (assume t889.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))))
% 2.41/2.69  (step t889.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.not tptp.falsehood)) (:= Z (tptp.not tptp.truth))))
% 2.41/2.69  (step t889.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) :rule or :premises (t889.t1))
% 2.41/2.69  (step t889.t3 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) :rule resolution :premises (t889.t2 t889.a0))
% 2.41/2.69  (step t889 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) :rule subproof :discharge (t889.a0))
% 2.41/2.69  (step t890 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) :rule resolution :premises (t888 t889))
% 2.41/2.69  (step t891 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))))) :rule implies_neg2)
% 2.41/2.69  (step t892 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))))) :rule resolution :premises (t890 t891))
% 2.41/2.69  (step t893 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth))))))) :rule contraction :premises (t892))
% 2.41/2.69  (step t894 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) :rule implies :premises (t893))
% 2.41/2.69  (step t895 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.truth (tptp.not tptp.falsehood)) (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth (tptp.not tptp.truth)))))) :rule resolution :premises (t894 t151))
% 2.41/2.69  (step t896 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t897)
% 2.41/2.69  (assume t897.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 2.41/2.69  (step t897.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)))) :rule forall_inst :args ((:= X tptp.falsehood)))
% 2.41/2.69  (step t897.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) :rule or :premises (t897.t1))
% 2.41/2.69  (step t897.t3 (cl (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) :rule resolution :premises (t897.t2 t897.a0))
% 2.41/2.69  (step t897 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) :rule subproof :discharge (t897.a0))
% 2.41/2.69  (step t898 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) :rule resolution :premises (t896 t897))
% 2.41/2.69  (step t899 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) (not (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)))) :rule implies_neg2)
% 2.41/2.69  (step t900 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)))) :rule resolution :premises (t898 t899))
% 2.41/2.69  (step t901 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood)))) :rule contraction :premises (t900))
% 2.41/2.69  (step t902 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) :rule implies :premises (t901))
% 2.41/2.69  (step t903 (cl (= tptp.falsehood (tptp.implies tptp.truth tptp.falsehood))) :rule resolution :premises (t902 t162))
% 2.41/2.69  (step t904 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t905)
% 2.41/2.69  (assume t905.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))))
% 2.41/2.69  (step t905.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t905.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) :rule or :premises (t905.t1))
% 2.41/2.69  (step t905.t3 (cl (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) :rule resolution :premises (t905.t2 t905.a0))
% 2.41/2.69  (step t905 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) :rule subproof :discharge (t905.a0))
% 2.41/2.69  (step t906 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) :rule resolution :premises (t904 t905))
% 2.41/2.69  (step t907 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) (not (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t908 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t906 t907))
% 2.41/2.69  (step t909 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood)))))) :rule contraction :premises (t908))
% 2.41/2.69  (step t910 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) :rule implies :premises (t909))
% 2.41/2.69  (step t911 (cl (= (tptp.xor tptp.truth (tptp.not tptp.falsehood)) (tptp.or (tptp.and tptp.truth (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not tptp.truth) (tptp.not tptp.falsehood))))) :rule resolution :premises (t910 a10))
% 2.41/2.69  (step t912 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t913)
% 2.41/2.69  (assume t913.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))))
% 2.41/2.69  (step t913.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y tptp.truth)))
% 2.41/2.69  (step t913.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule or :premises (t913.t1))
% 2.41/2.69  (step t913.t3 (cl (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule resolution :premises (t913.t2 t913.a0))
% 2.41/2.69  (step t913 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule subproof :discharge (t913.a0))
% 2.41/2.69  (step t914 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule resolution :premises (t912 t913))
% 2.41/2.69  (step t915 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) (not (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))))) :rule implies_neg2)
% 2.41/2.69  (step t916 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))))) :rule resolution :premises (t914 t915))
% 2.41/2.69  (step t917 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth))))) :rule contraction :premises (t916))
% 2.41/2.69  (step t918 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule implies :premises (t917))
% 2.41/2.69  (step t919 (cl (= (tptp.xor (tptp.not tptp.falsehood) tptp.truth) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.and (tptp.not (tptp.not tptp.falsehood)) tptp.truth)))) :rule resolution :premises (t918 a10))
% 2.41/2.69  (step t920 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t921)
% 2.41/2.69  (assume t921.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t921.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y (tptp.not (tptp.not tptp.falsehood)))))
% 2.41/2.69  (step t921.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule or :premises (t921.t1))
% 2.41/2.69  (step t921.t3 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule resolution :premises (t921.t2 t921.a0))
% 2.41/2.69  (step t921 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule subproof :discharge (t921.a0))
% 2.41/2.69  (step t922 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule resolution :premises (t920 t921))
% 2.41/2.69  (step t923 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (not (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule implies_neg2)
% 2.41/2.69  (step t924 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule resolution :premises (t922 t923))
% 2.41/2.69  (step t925 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule contraction :premises (t924))
% 2.41/2.69  (step t926 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule implies :premises (t925))
% 2.41/2.69  (step t927 (cl (= (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))) :rule resolution :premises (t926 a9))
% 2.41/2.69  (step t928 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t929)
% 2.41/2.69  (assume t929.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t929.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule forall_inst :args ((:= X (tptp.not tptp.x)) (:= Y (tptp.not (tptp.not tptp.x)))))
% 2.41/2.69  (step t929.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule or :premises (t929.t1))
% 2.41/2.69  (step t929.t3 (cl (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule resolution :premises (t929.t2 t929.a0))
% 2.41/2.69  (step t929 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule subproof :discharge (t929.a0))
% 2.41/2.69  (step t930 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule resolution :premises (t928 t929))
% 2.41/2.69  (step t931 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule implies_neg2)
% 2.41/2.69  (step t932 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule resolution :premises (t930 t931))
% 2.41/2.69  (step t933 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule contraction :premises (t932))
% 2.41/2.69  (step t934 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule implies :premises (t933))
% 2.41/2.69  (step t935 (cl (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))) :rule resolution :premises (t934 a9))
% 2.41/2.69  (step t936 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule equiv_pos2)
% 2.41/2.69  (step t937 (cl (= (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule all_simplify)
% 2.41/2.69  (step t938 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule cong :premises (t401 t937))
% 2.41/2.69  (step t939 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t940)
% 2.41/2.69  (assume t940.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t940.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (:= Y (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.41/2.69  (step t940.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule or :premises (t940.t1))
% 2.41/2.69  (step t940.t3 (cl (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t940.t2 t940.a0))
% 2.41/2.69  (step t940 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule subproof :discharge (t940.a0))
% 2.41/2.69  (step t941 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t939 t940))
% 2.41/2.69  (step t942 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies_neg2)
% 2.41/2.69  (step t943 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t941 t942))
% 2.41/2.69  (step t944 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule contraction :premises (t943))
% 2.41/2.69  (step t945 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t936 t938 t944))
% 2.41/2.69  (step t946 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule implies :premises (t945))
% 2.41/2.69  (step t947 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.and (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule resolution :premises (t946 a9))
% 2.41/2.69  (step t948 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t949)
% 2.41/2.69  (assume t949.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t949.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule forall_inst :args ((:= X tptp.x) (:= Y (tptp.not tptp.x))))
% 2.41/2.69  (step t949.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) :rule or :premises (t949.t1))
% 2.41/2.69  (step t949.t3 (cl (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) :rule resolution :premises (t949.t2 t949.a0))
% 2.41/2.69  (step t949 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) :rule subproof :discharge (t949.a0))
% 2.41/2.69  (step t950 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) :rule resolution :premises (t948 t949))
% 2.41/2.69  (step t951 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule implies_neg2)
% 2.41/2.69  (step t952 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule resolution :premises (t950 t951))
% 2.41/2.69  (step t953 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x)))) :rule contraction :premises (t952))
% 2.41/2.69  (step t954 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) :rule implies :premises (t953))
% 2.41/2.69  (step t955 (cl (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.and (tptp.not tptp.x) tptp.x))) :rule resolution :premises (t954 a9))
% 2.41/2.69  (step t956 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t957)
% 2.41/2.69  (assume t957.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t957.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t957.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) :rule or :premises (t957.t1))
% 2.41/2.69  (step t957.t3 (cl (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) :rule resolution :premises (t957.t2 t957.a0))
% 2.41/2.69  (step t957 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) :rule subproof :discharge (t957.a0))
% 2.41/2.69  (step t958 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) :rule resolution :premises (t956 t957))
% 2.41/2.69  (step t959 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) (not (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)))) :rule implies_neg2)
% 2.41/2.69  (step t960 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)))) :rule resolution :premises (t958 t959))
% 2.41/2.69  (step t961 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood)))) :rule contraction :premises (t960))
% 2.41/2.69  (step t962 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) :rule implies :premises (t961))
% 2.41/2.69  (step t963 (cl (= (tptp.and tptp.falsehood (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) tptp.falsehood))) :rule resolution :premises (t962 a9))
% 2.41/2.69  (step t964 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t965)
% 2.41/2.69  (assume t965.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))))
% 2.41/2.69  (step t965.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.not tptp.truth))))
% 2.41/2.69  (step t965.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule or :premises (t965.t1))
% 2.41/2.69  (step t965.t3 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule resolution :premises (t965.t2 t965.a0))
% 2.41/2.69  (step t965 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule subproof :discharge (t965.a0))
% 2.41/2.69  (step t966 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule resolution :premises (t964 t965))
% 2.41/2.69  (step t967 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule implies_neg2)
% 2.41/2.69  (step t968 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule resolution :premises (t966 t967))
% 2.41/2.69  (step t969 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule contraction :premises (t968))
% 2.41/2.69  (step t970 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.and Y X)))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule implies :premises (t969))
% 2.41/2.69  (step t971 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))) :rule resolution :premises (t970 a9))
% 2.41/2.69  (step t972 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t973)
% 2.41/2.69  (assume t973.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.69  (step t973.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (:= Y tptp.falsehood) (:= Z tptp.x)))
% 2.41/2.69  (step t973.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) :rule or :premises (t973.t1))
% 2.41/2.69  (step t973.t3 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) :rule resolution :premises (t973.t2 t973.a0))
% 2.41/2.69  (step t973 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) :rule subproof :discharge (t973.a0))
% 2.41/2.69  (step t974 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) :rule resolution :premises (t972 t973))
% 2.41/2.69  (step t975 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) (not (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))))) :rule implies_neg2)
% 2.41/2.69  (step t976 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))))) :rule resolution :premises (t974 t975))
% 2.41/2.69  (step t977 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x))))) :rule contraction :premises (t976))
% 2.41/2.69  (step t978 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) :rule implies :premises (t977))
% 2.41/2.69  (step t979 (cl (= (tptp.and (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) tptp.falsehood) tptp.x) (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.and tptp.falsehood tptp.x)))) :rule resolution :premises (t978 a8))
% 2.41/2.69  (step t980 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t981)
% 2.41/2.69  (assume t981.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))))
% 2.41/2.69  (step t981.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y tptp.x) (:= Z (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))
% 2.41/2.69  (step t981.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule or :premises (t981.t1))
% 2.41/2.69  (step t981.t3 (cl (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t981.t2 t981.a0))
% 2.41/2.69  (step t981 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule subproof :discharge (t981.a0))
% 2.41/2.69  (step t982 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t980 t981))
% 2.41/2.69  (step t983 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule implies_neg2)
% 2.41/2.69  (step t984 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule resolution :premises (t982 t983))
% 2.41/2.69  (step t985 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z)))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))) :rule contraction :premises (t984))
% 2.41/2.69  (step t986 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and (tptp.and X Y) Z) (tptp.and X (tptp.and Y Z))))) (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule implies :premises (t985))
% 2.41/2.69  (step t987 (cl (= (tptp.and (tptp.and tptp.falsehood tptp.x) (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.falsehood (tptp.and tptp.x (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t986 a8))
% 2.41/2.69  (step t988 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t989)
% 2.41/2.69  (assume t989.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t989.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not tptp.falsehood))) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t989.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) :rule or :premises (t989.t1))
% 2.41/2.69  (step t989.t3 (cl (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t989.t2 t989.a0))
% 2.41/2.69  (step t989 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) :rule subproof :discharge (t989.a0))
% 2.41/2.69  (step t990 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t988 t989))
% 2.41/2.69  (step t991 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))))) :rule implies_neg2)
% 2.41/2.69  (step t992 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))))) :rule resolution :premises (t990 t991))
% 2.41/2.69  (step t993 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood))))))) :rule contraction :premises (t992))
% 2.41/2.69  (step t994 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) :rule implies :premises (t993))
% 2.41/2.69  (step t995 (cl (= (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.falsehood))) (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t994 a7))
% 2.41/2.69  (step t996 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t997)
% 2.41/2.69  (assume t997.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t997.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not tptp.x))) (:= Y (tptp.not tptp.x))))
% 2.41/2.69  (step t997.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) :rule or :premises (t997.t1))
% 2.41/2.69  (step t997.t3 (cl (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t997.t2 t997.a0))
% 2.41/2.69  (step t997 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) :rule subproof :discharge (t997.a0))
% 2.41/2.69  (step t998 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t996 t997))
% 2.41/2.69  (step t999 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))))) :rule implies_neg2)
% 2.41/2.69  (step t1000 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t998 t999))
% 2.41/2.69  (step t1001 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x))))))) :rule contraction :premises (t1000))
% 2.41/2.69  (step t1002 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) :rule implies :premises (t1001))
% 2.41/2.69  (step t1003 (cl (= (tptp.and (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t1002 a7))
% 2.41/2.69  (step t1004 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1005)
% 2.41/2.69  (assume t1005.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t1005.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (:= Y (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))
% 2.41/2.69  (step t1005.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule or :premises (t1005.t1))
% 2.41/2.69  (step t1005.t3 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t1005.t2 t1005.a0))
% 2.41/2.69  (step t1005 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule subproof :discharge (t1005.a0))
% 2.41/2.69  (step t1006 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t1004 t1005))
% 2.41/2.69  (step t1007 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (not (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule implies_neg2)
% 2.41/2.69  (step t1008 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule resolution :premises (t1006 t1007))
% 2.41/2.69  (step t1009 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))))))) :rule contraction :premises (t1008))
% 2.41/2.69  (step t1010 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule implies :premises (t1009))
% 2.41/2.69  (step t1011 (cl (= (tptp.and (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.not (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))))) :rule resolution :premises (t1010 a7))
% 2.41/2.69  (step t1012 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1013)
% 2.41/2.69  (assume t1013.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t1013.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y tptp.falsehood)))
% 2.41/2.69  (step t1013.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule or :premises (t1013.t1))
% 2.41/2.69  (step t1013.t3 (cl (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1013.t2 t1013.a0))
% 2.41/2.69  (step t1013 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule subproof :discharge (t1013.a0))
% 2.41/2.69  (step t1014 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1012 t1013))
% 2.41/2.69  (step t1015 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t1016 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t1014 t1015))
% 2.41/2.69  (step t1017 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))) :rule contraction :premises (t1016))
% 2.41/2.69  (step t1018 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule implies :premises (t1017))
% 2.41/2.69  (step t1019 (cl (= (tptp.and (tptp.not tptp.falsehood) tptp.falsehood) (tptp.not (tptp.or (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1018 a7))
% 2.41/2.69  (step t1020 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1021)
% 2.41/2.69  (assume t1021.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t1021.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule forall_inst :args ((:= X (tptp.not tptp.x)) (:= Y (tptp.not (tptp.not tptp.x)))))
% 2.41/2.69  (step t1021.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule or :premises (t1021.t1))
% 2.41/2.69  (step t1021.t3 (cl (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t1021.t2 t1021.a0))
% 2.41/2.69  (step t1021 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule subproof :discharge (t1021.a0))
% 2.41/2.69  (step t1022 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t1020 t1021))
% 2.41/2.69  (step t1023 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (not (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule implies_neg2)
% 2.41/2.69  (step t1024 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule resolution :premises (t1022 t1023))
% 2.41/2.69  (step t1025 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x)))))))) :rule contraction :premises (t1024))
% 2.41/2.69  (step t1026 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule implies :premises (t1025))
% 2.41/2.69  (step t1027 (cl (= (tptp.and (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t1026 a7))
% 2.41/2.69  (step t1028 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1029)
% 2.41/2.69  (assume t1029.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t1029.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))))) :rule forall_inst :args ((:= X (tptp.not tptp.x)) (:= Y tptp.x)))
% 2.41/2.69  (step t1029.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule or :premises (t1029.t1))
% 2.41/2.69  (step t1029.t3 (cl (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule resolution :premises (t1029.t2 t1029.a0))
% 2.41/2.69  (step t1029 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule subproof :discharge (t1029.a0))
% 2.41/2.69  (step t1030 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule resolution :premises (t1028 t1029))
% 2.41/2.69  (step t1031 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) (not (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))))) :rule implies_neg2)
% 2.41/2.69  (step t1032 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))))) :rule resolution :premises (t1030 t1031))
% 2.41/2.69  (step t1033 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x)))))) :rule contraction :premises (t1032))
% 2.41/2.69  (step t1034 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule implies :premises (t1033))
% 2.41/2.69  (step t1035 (cl (= (tptp.and (tptp.not tptp.x) tptp.x) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.x))))) :rule resolution :premises (t1034 a7))
% 2.41/2.69  (step t1036 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1037)
% 2.41/2.69  (assume t1037.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t1037.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))))) :rule forall_inst :args ((:= X tptp.x) (:= Y (tptp.not tptp.x))))
% 2.41/2.69  (step t1037.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule or :premises (t1037.t1))
% 2.41/2.69  (step t1037.t3 (cl (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t1037.t2 t1037.a0))
% 2.41/2.69  (step t1037 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule subproof :discharge (t1037.a0))
% 2.41/2.69  (step t1038 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t1036 t1037))
% 2.41/2.69  (step t1039 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) (not (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))))) :rule implies_neg2)
% 2.41/2.69  (step t1040 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))))) :rule resolution :premises (t1038 t1039))
% 2.41/2.69  (step t1041 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))))) :rule contraction :premises (t1040))
% 2.41/2.69  (step t1042 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule implies :premises (t1041))
% 2.41/2.69  (step t1043 (cl (= (tptp.and tptp.x (tptp.not tptp.x)) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t1042 a7))
% 2.41/2.69  (step t1044 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1045)
% 2.41/2.69  (assume t1045.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t1045.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) :rule forall_inst :args ((:= X (tptp.not tptp.truth)) (:= Y tptp.truth)))
% 2.41/2.69  (step t1045.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) :rule or :premises (t1045.t1))
% 2.41/2.69  (step t1045.t3 (cl (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) :rule resolution :premises (t1045.t2 t1045.a0))
% 2.41/2.69  (step t1045 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) :rule subproof :discharge (t1045.a0))
% 2.41/2.69  (step t1046 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) :rule resolution :premises (t1044 t1045))
% 2.41/2.69  (step t1047 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) :rule implies_neg2)
% 2.41/2.69  (step t1048 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) :rule resolution :premises (t1046 t1047))
% 2.41/2.69  (step t1049 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth)))))) :rule contraction :premises (t1048))
% 2.41/2.69  (step t1050 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) :rule implies :premises (t1049))
% 2.41/2.69  (step t1051 (cl (= (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.truth)) (tptp.not tptp.truth))))) :rule resolution :premises (t1050 a7))
% 2.41/2.69  (step t1052 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1053)
% 2.41/2.69  (assume t1053.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t1053.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.not tptp.truth))))
% 2.41/2.69  (step t1053.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule or :premises (t1053.t1))
% 2.41/2.69  (step t1053.t3 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule resolution :premises (t1053.t2 t1053.a0))
% 2.41/2.69  (step t1053 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule subproof :discharge (t1053.a0))
% 2.41/2.69  (step t1054 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule resolution :premises (t1052 t1053))
% 2.41/2.69  (step t1055 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (not (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))))) :rule implies_neg2)
% 2.41/2.69  (step t1056 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))))) :rule resolution :premises (t1054 t1055))
% 2.41/2.69  (step t1057 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth))))))) :rule contraction :premises (t1056))
% 2.41/2.69  (step t1058 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule implies :premises (t1057))
% 2.41/2.69  (step t1059 (cl (= (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.not (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.truth)))))) :rule resolution :premises (t1058 a7))
% 2.41/2.69  (step t1060 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1061)
% 2.41/2.69  (assume t1061.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t1061.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))))) :rule forall_inst :args ((:= X (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))) (:= Y (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))
% 2.41/2.69  (step t1061.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) :rule or :premises (t1061.t1))
% 2.41/2.69  (step t1061.t3 (cl (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t1061.t2 t1061.a0))
% 2.41/2.69  (step t1061 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) :rule subproof :discharge (t1061.a0))
% 2.41/2.69  (step t1062 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t1060 t1061))
% 2.41/2.69  (step t1063 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) (not (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))))) :rule implies_neg2)
% 2.41/2.69  (step t1064 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))))) :rule resolution :premises (t1062 t1063))
% 2.41/2.69  (step t1065 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))))))) :rule contraction :premises (t1064))
% 2.41/2.69  (step t1066 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) :rule implies :premises (t1065))
% 2.41/2.69  (step t1067 (cl (= (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))) (tptp.or (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)) (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood)))))) :rule resolution :premises (t1066 a6))
% 2.41/2.69  (step t1068 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1069)
% 2.41/2.69  (assume t1069.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t1069.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule forall_inst :args ((:= X (tptp.and tptp.truth (tptp.not tptp.truth))) (:= Y (tptp.and (tptp.not tptp.truth) tptp.truth))))
% 2.41/2.69  (step t1069.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule or :premises (t1069.t1))
% 2.41/2.69  (step t1069.t3 (cl (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule resolution :premises (t1069.t2 t1069.a0))
% 2.41/2.69  (step t1069 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule subproof :discharge (t1069.a0))
% 2.41/2.69  (step t1070 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule resolution :premises (t1068 t1069))
% 2.41/2.69  (step t1071 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule implies_neg2)
% 2.41/2.69  (step t1072 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule resolution :premises (t1070 t1071))
% 2.41/2.69  (step t1073 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth)))))) :rule contraction :premises (t1072))
% 2.41/2.69  (step t1074 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule implies :premises (t1073))
% 2.41/2.69  (step t1075 (cl (= (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.truth) tptp.truth) (tptp.and tptp.truth (tptp.not tptp.truth))))) :rule resolution :premises (t1074 a6))
% 2.41/2.69  (step t1076 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1077)
% 2.41/2.69  (assume t1077.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t1077.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not tptp.x))) (:= Y (tptp.not tptp.truth))))
% 2.41/2.69  (step t1077.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) :rule or :premises (t1077.t1))
% 2.41/2.69  (step t1077.t3 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) :rule resolution :premises (t1077.t2 t1077.a0))
% 2.41/2.69  (step t1077 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) :rule subproof :discharge (t1077.a0))
% 2.41/2.69  (step t1078 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) :rule resolution :premises (t1076 t1077))
% 2.41/2.69  (step t1079 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))))) :rule implies_neg2)
% 2.41/2.69  (step t1080 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t1078 t1079))
% 2.41/2.69  (step t1081 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x)))))) :rule contraction :premises (t1080))
% 2.41/2.69  (step t1082 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) :rule implies :premises (t1081))
% 2.41/2.69  (step t1083 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.or (tptp.not tptp.truth) (tptp.not (tptp.not tptp.x))))) :rule resolution :premises (t1082 a6))
% 2.41/2.69  (step t1084 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1085)
% 2.41/2.69  (assume t1085.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t1085.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.not tptp.x))))
% 2.41/2.69  (step t1085.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) :rule or :premises (t1085.t1))
% 2.41/2.69  (step t1085.t3 (cl (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) :rule resolution :premises (t1085.t2 t1085.a0))
% 2.41/2.69  (step t1085 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) :rule subproof :discharge (t1085.a0))
% 2.41/2.69  (step t1086 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) :rule resolution :premises (t1084 t1085))
% 2.41/2.69  (step t1087 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) (not (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)))) :rule implies_neg2)
% 2.41/2.69  (step t1088 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)))) :rule resolution :premises (t1086 t1087))
% 2.41/2.69  (step t1089 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth)))) :rule contraction :premises (t1088))
% 2.41/2.69  (step t1090 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) :rule implies :premises (t1089))
% 2.41/2.69  (step t1091 (cl (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.or (tptp.not tptp.x) tptp.truth))) :rule resolution :premises (t1090 a6))
% 2.41/2.69  (step t1092 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule equiv_pos2)
% 2.41/2.69  (step t1093 (cl (= (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x)))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule all_simplify)
% 2.41/2.69  (step t1094 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))))) :rule cong :premises (t560 t1093))
% 2.41/2.69  (step t1095 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1096)
% 2.41/2.69  (assume t1096.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t1096.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x)))))) :rule forall_inst :args ((:= X (tptp.not tptp.x)) (:= Y (tptp.not (tptp.not tptp.x)))))
% 2.41/2.69  (step t1096.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))))) :rule or :premises (t1096.t1))
% 2.41/2.69  (step t1096.t3 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))))) :rule resolution :premises (t1096.t2 t1096.a0))
% 2.41/2.69  (step t1096 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))))) :rule subproof :discharge (t1096.a0))
% 2.41/2.69  (step t1097 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))))) :rule resolution :premises (t1095 t1096))
% 2.41/2.69  (step t1098 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x)))))) :rule implies_neg2)
% 2.41/2.69  (step t1099 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t1097 t1098))
% 2.41/2.69  (step t1100 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x)))))) :rule contraction :premises (t1099))
% 2.41/2.69  (step t1101 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x)))))) :rule resolution :premises (t1092 t1094 t1100))
% 2.41/2.69  (step t1102 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) :rule implies :premises (t1101))
% 2.41/2.69  (step t1103 (cl (= (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not (tptp.not tptp.x))) (tptp.or (tptp.not tptp.x) (tptp.not (tptp.not tptp.x))))) :rule resolution :premises (t1102 a4))
% 2.41/2.69  (step t1104 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))))) :rule equiv_pos2)
% 2.41/2.69  (step t1105 (cl (= (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))))) :rule all_simplify)
% 2.41/2.69  (step t1106 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))))) :rule cong :premises (t560 t1105))
% 2.41/2.69  (step t1107 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1108)
% 2.41/2.69  (assume t1108.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t1108.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t1108.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) :rule or :premises (t1108.t1))
% 2.41/2.69  (step t1108.t3 (cl (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) :rule resolution :premises (t1108.t2 t1108.a0))
% 2.41/2.69  (step t1108 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) :rule subproof :discharge (t1108.a0))
% 2.41/2.69  (step t1109 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) :rule resolution :premises (t1107 t1108))
% 2.41/2.69  (step t1110 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (not (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule implies_neg2)
% 2.41/2.69  (step t1111 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1109 t1110))
% 2.41/2.69  (step t1112 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.falsehood (tptp.not tptp.falsehood)) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule contraction :premises (t1111))
% 2.41/2.69  (step t1113 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood))))) :rule resolution :premises (t1104 t1106 t1112))
% 2.41/2.69  (step t1114 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))) :rule implies :premises (t1113))
% 2.41/2.69  (step t1115 (cl (= (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or tptp.falsehood (tptp.not tptp.falsehood)))) :rule resolution :premises (t1114 a4))
% 2.41/2.69  (step t1116 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1117)
% 2.41/2.69  (assume t1117.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t1117.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule forall_inst :args ((:= X (tptp.and (tptp.not tptp.x) tptp.truth)) (:= Y (tptp.and tptp.x (tptp.not tptp.truth)))))
% 2.41/2.69  (step t1117.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule or :premises (t1117.t1))
% 2.41/2.69  (step t1117.t3 (cl (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t1117.t2 t1117.a0))
% 2.41/2.69  (step t1117 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule subproof :discharge (t1117.a0))
% 2.41/2.69  (step t1118 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t1116 t1117))
% 2.41/2.69  (step t1119 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule implies_neg2)
% 2.41/2.69  (step t1120 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t1118 t1119))
% 2.41/2.69  (step t1121 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule contraction :premises (t1120))
% 2.41/2.69  (step t1122 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule implies :premises (t1121))
% 2.41/2.69  (step t1123 (cl (= (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.implies (tptp.not (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t1122 a4))
% 2.41/2.69  (step t1124 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1125)
% 2.41/2.69  (assume t1125.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t1125.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))))) :rule forall_inst :args ((:= X (tptp.not (tptp.not tptp.x))) (:= Y (tptp.not tptp.truth))))
% 2.41/2.69  (step t1125.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) :rule or :premises (t1125.t1))
% 2.41/2.69  (step t1125.t3 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) :rule resolution :premises (t1125.t2 t1125.a0))
% 2.41/2.69  (step t1125 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) :rule subproof :discharge (t1125.a0))
% 2.41/2.69  (step t1126 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) :rule resolution :premises (t1124 t1125))
% 2.41/2.69  (step t1127 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) (not (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))))) :rule implies_neg2)
% 2.41/2.69  (step t1128 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))))) :rule resolution :premises (t1126 t1127))
% 2.41/2.69  (step t1129 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth))))) :rule contraction :premises (t1128))
% 2.41/2.69  (step t1130 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) :rule implies :premises (t1129))
% 2.41/2.69  (step t1131 (cl (= (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)) (tptp.implies (tptp.not (tptp.not (tptp.not tptp.x))) (tptp.not tptp.truth)))) :rule resolution :premises (t1130 a4))
% 2.41/2.69  (step t1132 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1133)
% 2.41/2.69  (assume t1133.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))))
% 2.41/2.69  (step t1133.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y tptp.truth)))
% 2.41/2.69  (step t1133.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) :rule or :premises (t1133.t1))
% 2.41/2.69  (step t1133.t3 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) :rule resolution :premises (t1133.t2 t1133.a0))
% 2.41/2.69  (step t1133 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) :rule subproof :discharge (t1133.a0))
% 2.41/2.69  (step t1134 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) :rule resolution :premises (t1132 t1133))
% 2.41/2.69  (step t1135 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))))) :rule implies_neg2)
% 2.41/2.69  (step t1136 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))))) :rule resolution :premises (t1134 t1135))
% 2.41/2.69  (step t1137 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood))))) :rule contraction :premises (t1136))
% 2.41/2.69  (step t1138 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) :rule implies :premises (t1137))
% 2.41/2.69  (step t1139 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.truth)) (tptp.implies tptp.truth tptp.falsehood)))) :rule resolution :premises (t1138 t350))
% 2.41/2.69  (step t1140 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.truth (tptp.implies tptp.truth tptp.truth))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1141)
% 2.41/2.69  (assume t1141.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 2.41/2.69  (step t1141.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth)))
% 2.41/2.69  (step t1141.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth))) :rule or :premises (t1141.t1))
% 2.41/2.69  (step t1141.t3 (cl (= tptp.truth (tptp.implies tptp.truth tptp.truth))) :rule resolution :premises (t1141.t2 t1141.a0))
% 2.41/2.69  (step t1141 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth))) :rule subproof :discharge (t1141.a0))
% 2.41/2.69  (step t1142 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.truth (tptp.implies tptp.truth tptp.truth))) (= tptp.truth (tptp.implies tptp.truth tptp.truth))) :rule resolution :premises (t1140 t1141))
% 2.41/2.69  (step t1143 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.truth (tptp.implies tptp.truth tptp.truth))) (not (= tptp.truth (tptp.implies tptp.truth tptp.truth)))) :rule implies_neg2)
% 2.41/2.69  (step t1144 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.truth (tptp.implies tptp.truth tptp.truth))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)))) :rule resolution :premises (t1142 t1143))
% 2.41/2.69  (step t1145 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.truth (tptp.implies tptp.truth tptp.truth)))) :rule contraction :premises (t1144))
% 2.41/2.69  (step t1146 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.truth (tptp.implies tptp.truth tptp.truth))) :rule implies :premises (t1145))
% 2.41/2.69  (step t1147 (cl (= tptp.truth (tptp.implies tptp.truth tptp.truth))) :rule resolution :premises (t1146 t162))
% 2.41/2.69  (step t1148 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1149)
% 2.41/2.69  (assume t1149.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))))
% 2.41/2.69  (step t1149.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t1149.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule or :premises (t1149.t1))
% 2.41/2.69  (step t1149.t3 (cl (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1149.t2 t1149.a0))
% 2.41/2.69  (step t1149 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule subproof :discharge (t1149.a0))
% 2.41/2.69  (step t1150 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1148 t1149))
% 2.41/2.69  (step t1151 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (not (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t1152 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t1150 t1151))
% 2.41/2.69  (step t1153 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood)))))) :rule contraction :premises (t1152))
% 2.41/2.69  (step t1154 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule implies :premises (t1153))
% 2.41/2.69  (step t1155 (cl (= (tptp.xor (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)) (tptp.or (tptp.and (tptp.not tptp.falsehood) (tptp.not (tptp.not tptp.falsehood))) (tptp.and (tptp.not (tptp.not tptp.falsehood)) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1154 a10))
% 2.41/2.69  (step t1156 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1157)
% 2.41/2.69  (assume t1157.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))))
% 2.41/2.69  (step t1157.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule forall_inst :args ((:= X tptp.truth) (:= Y tptp.truth)))
% 2.41/2.69  (step t1157.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule or :premises (t1157.t1))
% 2.41/2.69  (step t1157.t3 (cl (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule resolution :premises (t1157.t2 t1157.a0))
% 2.41/2.69  (step t1157 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule subproof :discharge (t1157.a0))
% 2.41/2.69  (step t1158 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule resolution :premises (t1156 t1157))
% 2.41/2.69  (step t1159 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (not (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule implies_neg2)
% 2.41/2.69  (step t1160 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule resolution :premises (t1158 t1159))
% 2.41/2.69  (step t1161 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y)))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth))))) :rule contraction :premises (t1160))
% 2.41/2.69  (step t1162 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.or (tptp.and X (tptp.not Y)) (tptp.and (tptp.not X) Y))))) (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule implies :premises (t1161))
% 2.41/2.69  (step t1163 (cl (= (tptp.xor tptp.truth tptp.truth) (tptp.or (tptp.and tptp.truth (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.truth) tptp.truth)))) :rule resolution :premises (t1162 a10))
% 2.41/2.69  (step t1164 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1165)
% 2.41/2.69  (assume t1165.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t1165.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule forall_inst :args ((:= X (tptp.not tptp.x)) (:= Y tptp.truth)))
% 2.41/2.69  (step t1165.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule or :premises (t1165.t1))
% 2.41/2.69  (step t1165.t3 (cl (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule resolution :premises (t1165.t2 t1165.a0))
% 2.41/2.69  (step t1165 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule subproof :discharge (t1165.a0))
% 2.41/2.69  (step t1166 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule resolution :premises (t1164 t1165))
% 2.41/2.69  (step t1167 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) (not (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule implies_neg2)
% 2.41/2.69  (step t1168 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule resolution :premises (t1166 t1167))
% 2.41/2.69  (step t1169 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth)))))) :rule contraction :premises (t1168))
% 2.41/2.69  (step t1170 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule implies :premises (t1169))
% 2.41/2.69  (step t1171 (cl (= (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.not (tptp.or (tptp.not (tptp.not tptp.x)) (tptp.not tptp.truth))))) :rule resolution :premises (t1170 a7))
% 2.41/2.69  (step t1172 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1173)
% 2.41/2.69  (assume t1173.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t1173.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule forall_inst :args ((:= X (tptp.and tptp.x (tptp.not tptp.truth))) (:= Y (tptp.and (tptp.not tptp.x) tptp.truth))))
% 2.41/2.69  (step t1173.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule or :premises (t1173.t1))
% 2.41/2.69  (step t1173.t3 (cl (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t1173.t2 t1173.a0))
% 2.41/2.69  (step t1173 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule subproof :discharge (t1173.a0))
% 2.41/2.69  (step t1174 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t1172 t1173))
% 2.41/2.69  (step t1175 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule implies_neg2)
% 2.41/2.69  (step t1176 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule resolution :premises (t1174 t1175))
% 2.41/2.69  (step t1177 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth)))))) :rule contraction :premises (t1176))
% 2.41/2.69  (step t1178 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule implies :premises (t1177))
% 2.41/2.69  (step t1179 (cl (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.or (tptp.and (tptp.not tptp.x) tptp.truth) (tptp.and tptp.x (tptp.not tptp.truth))))) :rule resolution :premises (t1178 a6))
% 2.41/2.69  (step t1180 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))))) :rule equiv_pos2)
% 2.41/2.69  (step t1181 (cl (= (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))))) :rule all_simplify)
% 2.41/2.69  (step t1182 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x)))))) :rule cong :premises (t560 t1181))
% 2.41/2.69  (step t1183 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1184)
% 2.41/2.69  (assume t1184.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t1184.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x))))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.not tptp.x))))
% 2.41/2.69  (step t1184.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)))) :rule or :premises (t1184.t1))
% 2.41/2.69  (step t1184.t3 (cl (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)))) :rule resolution :premises (t1184.t2 t1184.a0))
% 2.41/2.69  (step t1184 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)))) :rule subproof :discharge (t1184.a0))
% 2.41/2.69  (step t1185 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)))) :rule resolution :premises (t1183 t1184))
% 2.41/2.69  (step t1186 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)))) (not (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x))))) :rule implies_neg2)
% 2.41/2.69  (step t1187 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x))))) :rule resolution :premises (t1185 t1186))
% 2.41/2.69  (step t1188 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or tptp.truth (tptp.not tptp.x)) (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x))))) :rule contraction :premises (t1187))
% 2.41/2.69  (step t1189 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x))))) :rule resolution :premises (t1180 t1182 t1188))
% 2.41/2.69  (step t1190 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x)))) :rule implies :premises (t1189))
% 2.41/2.69  (step t1191 (cl (= (tptp.implies (tptp.not tptp.truth) (tptp.not tptp.x)) (tptp.or tptp.truth (tptp.not tptp.x)))) :rule resolution :premises (t1190 a4))
% 2.41/2.69  (step t1192 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1193)
% 2.41/2.69  (assume t1193.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t1193.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule forall_inst :args ((:= X (tptp.and tptp.x (tptp.not tptp.truth))) (:= Y (tptp.and (tptp.not tptp.x) tptp.truth))))
% 2.41/2.69  (step t1193.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule or :premises (t1193.t1))
% 2.41/2.69  (step t1193.t3 (cl (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule resolution :premises (t1193.t2 t1193.a0))
% 2.41/2.69  (step t1193 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule subproof :discharge (t1193.a0))
% 2.41/2.69  (step t1194 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule resolution :premises (t1192 t1193))
% 2.41/2.69  (step t1195 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) (not (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule implies_neg2)
% 2.41/2.69  (step t1196 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule resolution :premises (t1194 t1195))
% 2.41/2.69  (step t1197 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth))))) :rule contraction :premises (t1196))
% 2.41/2.69  (step t1198 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule implies :premises (t1197))
% 2.41/2.69  (step t1199 (cl (= (tptp.or (tptp.and tptp.x (tptp.not tptp.truth)) (tptp.and (tptp.not tptp.x) tptp.truth)) (tptp.implies (tptp.not (tptp.and tptp.x (tptp.not tptp.truth))) (tptp.and (tptp.not tptp.x) tptp.truth)))) :rule resolution :premises (t1198 a4))
% 2.41/2.69  (step t1200 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1201)
% 2.41/2.69  (assume t1201.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))))
% 2.41/2.69  (step t1201.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X (tptp.not tptp.falsehood)) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t1201.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule or :premises (t1201.t1))
% 2.41/2.69  (step t1201.t3 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1201.t2 t1201.a0))
% 2.41/2.69  (step t1201 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule subproof :discharge (t1201.a0))
% 2.41/2.69  (step t1202 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1200 t1201))
% 2.41/2.69  (step t1203 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t1204 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t1202 t1203))
% 2.41/2.69  (step t1205 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood)))))) :rule contraction :premises (t1204))
% 2.41/2.69  (step t1206 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule implies :premises (t1205))
% 2.41/2.69  (step t1207 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.not (tptp.not tptp.falsehood)) (tptp.not (tptp.not tptp.falsehood))) (tptp.implies (tptp.not tptp.falsehood) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1206 t350))
% 2.41/2.69  (step t1208 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)))) :rule equiv_pos2)
% 2.41/2.69  (step t1209 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))) :rule refl)
% 2.41/2.69  (step t1210 (cl (= (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)))) :rule all_simplify)
% 2.41/2.69  (step t1211 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x))))) :rule cong :premises (t1209 t1210))
% 2.41/2.69  (step t1212 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1213)
% 2.41/2.69  (assume t1213.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t1213.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))))) :rule forall_inst :args ((:= X tptp.falsehood) (:= Y tptp.x)))
% 2.41/2.69  (step t1213.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule or :premises (t1213.t1))
% 2.41/2.69  (step t1213.t3 (cl (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule resolution :premises (t1213.t2 t1213.a0))
% 2.41/2.69  (step t1213 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule subproof :discharge (t1213.a0))
% 2.41/2.69  (step t1214 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule resolution :premises (t1212 t1213))
% 2.41/2.69  (step t1215 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) (not (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))))) :rule implies_neg2)
% 2.41/2.69  (step t1216 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))))) :rule resolution :premises (t1214 t1215))
% 2.41/2.69  (step t1217 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.falsehood tptp.x) (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))))) :rule contraction :premises (t1216))
% 2.41/2.69  (step t1218 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x)))) :rule resolution :premises (t1208 t1211 t1217))
% 2.41/2.69  (step t1219 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x))) :rule implies :premises (t1218))
% 2.41/2.69  (step t1220 (cl (= (tptp.not (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))) (tptp.and tptp.falsehood tptp.x))) :rule resolution :premises (t1219 a7))
% 2.41/2.69  (step t1221 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)))) :rule equiv_pos2)
% 2.41/2.69  (step t1222 (cl (= (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)))) :rule all_simplify)
% 2.41/2.69  (step t1223 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))))) :rule cong :premises (t1209 t1222))
% 2.41/2.69  (step t1224 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1225)
% 2.41/2.69  (assume t1225.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t1225.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X tptp.x) (:= Y tptp.falsehood)))
% 2.41/2.69  (step t1225.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule or :premises (t1225.t1))
% 2.41/2.69  (step t1225.t3 (cl (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1225.t2 t1225.a0))
% 2.41/2.69  (step t1225 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule subproof :discharge (t1225.a0))
% 2.41/2.69  (step t1226 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1224 t1225))
% 2.41/2.69  (step t1227 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t1228 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t1226 t1227))
% 2.41/2.69  (step t1229 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule contraction :premises (t1228))
% 2.41/2.69  (step t1230 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood)))) :rule resolution :premises (t1221 t1223 t1229))
% 2.41/2.69  (step t1231 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))) :rule implies :premises (t1230))
% 2.41/2.69  (step t1232 (cl (= (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))) (tptp.and tptp.x tptp.falsehood))) :rule resolution :premises (t1231 a7))
% 2.41/2.69  (step t1233 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1234)
% 2.41/2.69  (assume t1234.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))))
% 2.41/2.69  (step t1234.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule forall_inst :args ((:= X (tptp.not tptp.x)) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t1234.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule or :premises (t1234.t1))
% 2.41/2.69  (step t1234.t3 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule resolution :premises (t1234.t2 t1234.a0))
% 2.41/2.69  (step t1234 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule subproof :discharge (t1234.a0))
% 2.41/2.69  (step t1235 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule resolution :premises (t1233 t1234))
% 2.41/2.69  (step t1236 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule implies_neg2)
% 2.41/2.69  (step t1237 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule resolution :premises (t1235 t1236))
% 2.41/2.69  (step t1238 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x))))) :rule contraction :premises (t1237))
% 2.41/2.69  (step t1239 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.or Y X)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule implies :premises (t1238))
% 2.41/2.69  (step t1240 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.or (tptp.not tptp.falsehood) (tptp.not tptp.x)))) :rule resolution :premises (t1239 a6))
% 2.41/2.69  (step t1241 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1242)
% 2.41/2.69  (assume t1242.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))))
% 2.41/2.69  (step t1242.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))))) :rule forall_inst :args ((:= X (tptp.not tptp.x)) (:= Y (tptp.not tptp.falsehood))))
% 2.41/2.69  (step t1242.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) :rule or :premises (t1242.t1))
% 2.41/2.69  (step t1242.t3 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) :rule resolution :premises (t1242.t2 t1242.a0))
% 2.41/2.69  (step t1242 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) :rule subproof :discharge (t1242.a0))
% 2.41/2.69  (step t1243 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) :rule resolution :premises (t1241 t1242))
% 2.41/2.69  (step t1244 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) (not (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))))) :rule implies_neg2)
% 2.41/2.69  (step t1245 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1243 t1244))
% 2.41/2.69  (step t1246 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood))))) :rule contraction :premises (t1245))
% 2.41/2.69  (step t1247 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.or X Y) (tptp.implies (tptp.not X) Y)))) (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) :rule implies :premises (t1246))
% 2.41/2.69  (step t1248 (cl (= (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)) (tptp.implies (tptp.not (tptp.not tptp.x)) (tptp.not tptp.falsehood)))) :rule resolution :premises (t1247 a4))
% 2.41/2.69  (step t1249 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) :rule implies_neg1)
% 2.41/2.69  (anchor :step t1250)
% 2.41/2.69  (assume t1250.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))))
% 2.41/2.69  (step t1250.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule forall_inst :args ((:= X tptp.x) (:= Y tptp.falsehood)))
% 2.41/2.69  (step t1250.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule or :premises (t1250.t1))
% 2.41/2.69  (step t1250.t3 (cl (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1250.t2 t1250.a0))
% 2.41/2.69  (step t1250 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule subproof :discharge (t1250.a0))
% 2.41/2.69  (step t1251 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1249 t1250))
% 2.41/2.69  (step t1252 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (not (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule implies_neg2)
% 2.41/2.69  (step t1253 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule resolution :premises (t1251 t1252))
% 2.41/2.69  (step t1254 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood)))))) :rule contraction :premises (t1253))
% 2.41/2.69  (step t1255 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.not (tptp.or (tptp.not X) (tptp.not Y)))))) (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule implies :premises (t1254))
% 2.41/2.69  (step t1256 (cl (= (tptp.and_star tptp.x tptp.falsehood) (tptp.not (tptp.or (tptp.not tptp.x) (tptp.not tptp.falsehood))))) :rule resolution :premises (t1255 a12))
% 2.41/2.69  (step t1257 (cl (not (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))) :rule not_symm :premises (a16))
% 2.41/2.69  (step t1258 (cl (= tptp.falsehood (tptp.not tptp.truth))) :rule symm :premises (a15))
% 2.41/2.69  (step t1259 (cl) :rule resolution :premises (t141 t152 t163 t176 t188 t196 t204 t212 t220 t228 t236 t244 t252 t260 t268 t276 t284 t292 t300 t308 t316 t324 t332 t340 t351 t359 t367 t375 t383 t391 t399 t412 t424 t436 t449 t457 t465 t473 t481 t489 t497 t505 t513 t521 t529 t537 t550 t558 t571 t583 t591 t599 t607 t615 t623 t631 t639 t647 t655 t663 t671 t679 t691 t703 t715 t723 t731 t739 t747 t755 t763 t771 t779 t787 t795 t803 t815 t827 t839 t847 t855 t863 t871 t879 t887 t895 t903 t911 t919 t927 t935 t947 t955 t963 t971 t979 t987 t995 t1003 t1011 t1019 t1027 t1035 t1043 t1051 t1059 t1067 t1075 t1083 t1091 t1103 t1115 t1123 t1131 t1139 t1147 t1155 t1163 t1171 t1179 t1191 t1199 t1207 t1220 t1232 t1240 t1248 t1256 t1257 t1258))
% 2.41/2.69  
% 2.45/2.70  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.zmR6qYeA2M/cvc5---1.0.5_18335.smt2
% 2.45/2.70  % cvc5---1.0.5 exiting
% 2.45/2.70  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------